diff --git a/A_Getting_started_anyscript/lesson3.md b/A_Getting_started_anyscript/lesson3.md index afe2dbed..a8a683bd 100644 --- a/A_Getting_started_anyscript/lesson3.md +++ b/A_Getting_started_anyscript/lesson3.md @@ -1,6 +1,7 @@ ::: {rst-class} break ::: +(How_to_write_AnyScript_L3)= # Lesson 3: Connecting Segments by Joints :::{note} diff --git a/ForceDependentKinematics/Downloads/DemoSimpleKnee2.any b/ForceDependentKinematics/Downloads/DemoSimpleKnee2.any index 3ab268de..161e51d9 100644 --- a/ForceDependentKinematics/Downloads/DemoSimpleKnee2.any +++ b/ForceDependentKinematics/Downloads/DemoSimpleKnee2.any @@ -61,7 +61,7 @@ Main = { sRel = {0.0, 0.4, 0.0}; }; AnyRefNode Quadriceps = { - sRel={0.00, 0.3, 0.0}; + sRel={0.05, 0.3, 0.0}; }; }; diff --git a/ForceDependentKinematics/Downloads/DemoSimpleKnee3.any b/ForceDependentKinematics/Downloads/DemoSimpleKnee3.any index 689b05b2..3ab268de 100644 --- a/ForceDependentKinematics/Downloads/DemoSimpleKnee3.any +++ b/ForceDependentKinematics/Downloads/DemoSimpleKnee3.any @@ -41,7 +41,7 @@ Main = { // Origin of the quadriceps muscle. AnyRefNode Quadriceps = { - sRel = {0.00, 0.3, 0.0}; + sRel = {0.06, 0.0, 0.0}; }; AnyDrawSeg drw ={ Opacity = 0.5; diff --git a/ForceDependentKinematics/Downloads/DemoSimpleKnee4.any b/ForceDependentKinematics/Downloads/DemoSimpleKnee4.any index 816b2eae..df5a118b 100644 --- a/ForceDependentKinematics/Downloads/DemoSimpleKnee4.any +++ b/ForceDependentKinematics/Downloads/DemoSimpleKnee4.any @@ -53,7 +53,7 @@ Main = { // Origin of the quadriceps muscle. AnyRefNode Quadriceps = { - sRel = {0.00, 0.3, 0.0}; + sRel = {0.06, 0.0, 0.0}; }; AnyDrawSeg drw ={ Opacity = 0.5; diff --git a/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-1.any b/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-1.any new file mode 100644 index 00000000..a98bc854 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-1.any @@ -0,0 +1,139 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment + AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + }; + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + + AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + AnyRefNode Quadriceps = { + sRel={0.05, 0.3, 0.0}; + }; + }; + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. +//# BEGIN SNIPPET 1 +AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + §// Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + };§ +}; +//# END SNIPPET 1 + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-2.any b/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-2.any new file mode 100644 index 00000000..890e1118 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson2/snip.SimpleKnee.main-2.any @@ -0,0 +1,149 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment + AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + }; + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + + AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + AnyRefNode Quadriceps = { + sRel={0.05, 0.3, 0.0}; + }; + }; + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. +//# BEGIN SNIPPET 1 +AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; +}; +§// Define springs in the knee, simulating the effect of cartilage +// and ligaments. +AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; +};§ + +//# END SNIPPET 1 + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + +//# BEGIN SNIPPET 2 +AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + §InverseDynamics.ForceDepKinOnOff=On;§ +}; +//# END SNIPPET 2 + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson3/snip.SimpleKnee.main-1.any b/ForceDependentKinematics/Snippets/lesson3/snip.SimpleKnee.main-1.any new file mode 100644 index 00000000..7fb99065 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson3/snip.SimpleKnee.main-1.any @@ -0,0 +1,146 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment + AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + }; + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + +//# BEGIN SNIPPET 1 +AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + AnyRefNode Quadriceps = { + sRel={§0.00, 0.3, 0.0§}; + }; +}; +//# END SNIPPET 1 + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. + AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; + }; + // Define springs in the knee, simulating the effect of cartilage + // and ligaments. + AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; + }; + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + InverseDynamics.ForceDepKinOnOff=On; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson4/simplefemoral.stl b/ForceDependentKinematics/Snippets/lesson4/simplefemoral.stl new file mode 100644 index 00000000..66cc2ee4 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson4/simplefemoral.stl @@ -0,0 +1,64906 @@ +solid Main.MyModel.GlobalRef.SurfSTLCenter2.FemoralHead.drw +facet normal 0.000000000000000e+000 0.000000000000000e+000 -1.000000000000000e+000 + outer loop + vertex 2.897221183776855e-002 -7.274504184722900e-003 -3.816668319702148e-002 + vertex 3.189121055603027e-002 -7.274504184722900e-003 -3.816668319702148e-002 + vertex 3.189121055603027e-002 -1.024909210205078e-002 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0.000000000000000e+000 0.000000000000000e+000 1.000000000000000e+000 + outer loop + vertex -1.999193954467773e-002 2.143440723419190e-003 3.812601089477540e-002 + vertex -1.713571739196777e-002 4.595909118652344e-003 3.812601089477540e-002 + vertex -1.999193954467773e-002 4.595909118652344e-003 3.812601089477540e-002 + endloop +endfacet +facet normal 0.000000000000000e+000 0.000000000000000e+000 1.000000000000000e+000 + outer loop + vertex -2.284816169738770e-002 2.143440723419190e-003 3.812601089477540e-002 + vertex -1.999193954467773e-002 4.595909118652344e-003 3.812601089477540e-002 + vertex -2.284816169738770e-002 4.595909118652344e-003 3.812601089477540e-002 + endloop +endfacet +endsolid Main.MyModel.GlobalRef.SurfSTLCenter.TibialPartHead.drw diff --git a/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-1.any b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-1.any new file mode 100644 index 00000000..17b253e7 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-1.any @@ -0,0 +1,146 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment + AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + }; + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + +//# BEGIN SNIPPET 1 +AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + AnyRefNode Quadriceps = { + sRel={§0.05, 0.3, 0.0§}; + }; +}; +//# END SNIPPET 1 + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. + AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; + }; + // Define springs in the knee, simulating the effect of cartilage + // and ligaments. + AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; + }; + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + InverseDynamics.ForceDepKinOnOff=On; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-2.any b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-2.any new file mode 100644 index 00000000..d529a284 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-2.any @@ -0,0 +1,151 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment +//# BEGIN SNIPPET 1 +AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + §AnyDrawRefFrame drw = {RGB = {0,0,0}; ScaleXYZ = 0.05 * {1,1,1};};§ + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + }; +//# END SNIPPET 1 + + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + +//# BEGIN SNIPPET 2 +AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + §AnyDrawRefFrame drw = {RGB = {1,1,1}; ScaleXYZ = 0.05 * {1,1,1};};§ + }; + AnyRefNode Quadriceps = { + sRel={0.05, 0.3, 0.0}; + }; +}; +//# END SNIPPET 2 + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. + AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; + }; + // Define springs in the knee, simulating the effect of cartilage + // and ligaments. + AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; + }; + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + InverseDynamics.ForceDepKinOnOff=On; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-3.any b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-3.any new file mode 100644 index 00000000..76e2d202 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-3.any @@ -0,0 +1,170 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment +//# BEGIN SNIPPET 1 +AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + AnyDrawRefFrame drw = {RGB = {0,0,0}; ScaleXYZ = 0.05 * {1,1,1};}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + + §AnySurfSTL FemoralHead = { + FileName = "simplefemoral.stl"; + AnyDrawSurf drw = { + FileName = .FileName; + Opacity = 0.5; + }; + };§ + }; +//# END SNIPPET 1 + + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + +//# BEGIN SNIPPET 2 +AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + AnyDrawRefFrame drw = {RGB = {1,1,1}; ScaleXYZ = 0.05 * {1,1,1};}; + + §AnyRefNode SurfSTLCenter = { + sRel = {0.01,-0.04,0}; + AnySurfSTL TibialPlateau = { + FileName = "simpletibial.stl"; + AnyDrawSurf drw = { + FileName = .FileName; + Opacity = 0.5; + }; + }; + };§ + }; + AnyRefNode Quadriceps = { + sRel={0.05, 0.3, 0.0}; + }; +}; +//# END SNIPPET 2 + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. + AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; + }; + // Define springs in the knee, simulating the effect of cartilage + // and ligaments. + AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; + }; + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + InverseDynamics.ForceDepKinOnOff=On; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-4.any b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-4.any new file mode 100644 index 00000000..01035b68 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson4/snip.SimpleKnee.main-4.any @@ -0,0 +1,179 @@ +// This model is for the FDK tutorial. It is the starting point for the +//definition of a simple knee with force-dependent kinematics features. + +Main = { + + /// The actual body model goes in this folder + AnyFolder MyModel = { + + // Global Reference Frame + AnyFixedRefFrame GlobalRef = { + }; // Global reference frame + + // Definition of the thigh segment + AnySeg Thigh = { + r0 = {0.4, 0, 0}; + Axes0 = RotMat(pi/2,z); + Mass = 5; + Jii = {0.3, 0.01, 0.3}*0.7; + + // This is the center of the nominal knee joint. Notice that + // the actual knee center will vary when we use FDK. + AnyRefNode KneeCenter = { + sRel = {-0.03, -0.4, 0.0}; + AnyDrawRefFrame drw = {RGB = {0,0,0}; ScaleXYZ = 0.05 * {1,1,1};}; + + // Define a cylinder representing the femoral condyle. The quadriceps + // will wrap about this cylinder. + AnyRefNode SurfCenter = { + sRel = {0,0,-0.05}; + AnySurfCylinder Condyle = { + Radius = 0.06; + Length = 0.1; + AnyDrawParamSurf drw = { + RGB = {0, 0, 1}; + }; + }; + }; + + AnySurfSTL FemoralHead = { + FileName = "simplefemoral.stl"; + AnyDrawSurf drw = { + FileName = .FileName; + Opacity = 0.5; + }; + }; + }; + + AnyRefNode HipCenter = { + sRel = {0.0, 0.4, 0.0}; + }; + + // Origin of the quadriceps muscle. + AnyRefNode Quadriceps = { + sRel = {0.06, 0.0, 0.0}; + }; + AnyDrawSeg drw ={ + Opacity = 0.5; + }; + }; + + AnySeg Shank = { + r0 = {0.8, -0.4, 0.0}; + Mass = 4; + Jii = {0.4, 0.01, 0.4}*0.4; + AnyDrawSeg drw ={ + Opacity = 0.5; + RGB = {1,0,0}; + }; + + AnyRefNode KneeCenter = { + sRel = {0.0, 0.4, 0.0}; + AnyDrawRefFrame drw = {RGB = {1,1,1}; ScaleXYZ = 0.05 * {1,1,1};}; + + AnyRefNode SurfSTLCenter = { + sRel = {0.01,-0.04,0}; + AnySurfSTL TibialPlateau = { + FileName = "simpletibial.stl"; + AnyDrawSurf drw = { + FileName = .FileName; + Opacity = 0.5; + }; + }; + }; + }; + +//# BEGIN SNIPPET 1 + AnyRefNode Quadriceps = { + sRel={0.05, 0.3, 0.0}; + }; +}; //END of AnySeg Shank + +// Define a contact force between the STL surfaces of the femoral condyle and +// the tibial plateau to make these surfaces to make the surfaces slide along +// each other. +§AnyForceSurfaceContact ContactForce = { + AnySurface &surfMaster = .Thigh.KneeCenter.FemoralHead; + AnySurface &surfSlave = .Shank.KneeCenter.SurfSTLCenter.TibialPlateau; + PressureModule = 5e7; + ForceViewOnOff = On; +};§ +//# END SNIPPET 1 + + // Hip joint between the thigh and ground + AnyRevoluteJoint Hip = { + AnyRefFrame &ref1 = .GlobalRef; + AnyRefFrame &ref2 = .Thigh.HipCenter; + }; + + // Fix the hip joint at a constant angle + AnyKinEqSimpleDriver HipAngle = { + AnyRevoluteJoint &Hip = .Hip; + DriverPos = {pi/2}; + DriverVel = {0}; + }; + + // Knee joint. Notice that this is only going to be the nominal joint. + // The actual position of the knee joint center will depend on the forces + // acting upon it. Notice that we list the shank before the thigh. This + // defines the knee joint in the shank coordinate system and we can + // relate the reaction forces to the directon of the tibial plateau. + AnyRevoluteJoint KneeJoint = { + AnyRefFrame &Shank = .Shank.KneeCenter; + AnyRefFrame &Thigh = .Thigh.KneeCenter; + + // Prepare the joint for FDK: Define the reaction types in x and y + // directions to be FDK-dependent. These reaction forces must then + // be switched off and provided by some elastic element that we + // define explicitly below. + Constraints = { + CType = {ForceDep, ForceDep, Hard, Hard, Hard}; + Reaction.Type={Off,Off,On,On,On}; + }; + }; + // Define springs in the knee, simulating the effect of cartilage + // and ligaments. + AnyForce KneeStiffness = { + AnyKinLinear &lin = Main.MyModel.KneeJoint.Linear; + F = {-1000*lin.Pos[0], -5000*lin.Pos[1], 0}; + }; + + // Knee driver- just a simple knee extension. + AnyKinEqSimpleDriver KneeDriver = { + DriverPos = {pi/2}; + DriverVel = {-pi/30}; + AnyRevoluteJoint &KneeJoint = .KneeJoint; + Reaction.Type={Off}; // The muscles must carry this movement + }; + + // Muscle + AnyMuscleShortestPath Quadriceps = { + AnyMuscleModel MusMdl = { + F0 = 6000; + }; + AnyRefFrame &org = .Thigh.Quadriceps; + AnyParamSurf &wrap = .Thigh.KneeCenter.SurfCenter.Condyle; + AnyRefFrame &ins = .Shank.Quadriceps; + SPLine = { + StringMesh = 50; + InitWrapPosVectors = {{0.1, 0.1, 0},{0.1, 0.2, 0}}; + }; + AnyDrawMuscle drw = { + Bulging = 1; + MaxStress = 2500; + }; + }; + }; // MyModel + + AnyBodyStudy Study = { + AnyFolder &Model = .MyModel; + Gravity = {0.0, -9.81, 0.0}; + tStart = 1; + tEnd = 10; + nStep = 100; + InverseDynamics.ForceDepKinOnOff=On; + }; + +}; // Main + + diff --git a/ForceDependentKinematics/Snippets/lesson5/Input/FemImplant.anysurf3 b/ForceDependentKinematics/Snippets/lesson5/Input/FemImplant.anysurf3 new file mode 100644 index 00000000..c417a385 --- /dev/null +++ b/ForceDependentKinematics/Snippets/lesson5/Input/FemImplant.anysurf3 @@ -0,0 +1,32313 @@ +ANYSURF +FORMAT 3 +8841 17675 + 1.625000e-002 1.053555e-002 4.993958e-003 9.210390e-001 3.537881e-001 1.628528e-001 + 1.625000e-002 1.044985e-002 5.159306e-003 9.246263e-001 3.406549e-001 1.703540e-001 + 1.625000e-002 1.142688e-002 -2.316019e-003 9.940883e-001 1.060742e-001 -2.316872e-002 + 1.625000e-002 -4.668488e-003 1.067937e-002 9.468838e-001 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2.757150e-001 -1.000000e-004 +1997 1933 1934 -8.968582e-001 -3.458748e-001 2.757099e-001 -1.000000e-004 +1997 1934 1998 -9.159270e-001 -3.458748e-001 2.035886e-001 -1.000000e-004 +1998 1934 1935 -9.159262e-001 -3.458762e-001 2.035900e-001 -1.000000e-004 +1998 1935 1999 -9.292066e-001 -3.458762e-001 1.301719e-001 -1.000000e-004 +1999 1935 1936 -9.292055e-001 -3.458784e-001 1.301742e-001 -1.000000e-004 +1999 1936 2000 -9.366104e-001 -3.458785e-001 5.593749e-002 -1.000000e-004 +2000 1936 1937 -9.366120e-001 -3.458749e-001 5.593353e-002 -1.000000e-004 +2000 1937 2001 -9.380952e-001 -3.458749e-001 -1.865437e-002 -1.000000e-004 +2001 1937 1938 -9.380953e-001 -3.458745e-001 -1.865485e-002 -1.000000e-004 +2001 1938 2002 -9.336474e-001 -3.458744e-001 -9.313138e-002 -1.000000e-004 +2002 1938 1939 -9.336460e-001 -3.458798e-001 -9.312513e-002 -1.000000e-004 +2002 1939 2003 -9.232960e-001 -3.458799e-001 -1.670079e-001 -1.000000e-004 +2003 1939 1940 -9.232966e-001 -3.458759e-001 -1.670126e-001 -1.000000e-004 +2003 1940 2004 -9.071081e-001 -3.458758e-001 -2.398434e-001 -1.000000e-004 +2004 1940 1941 -9.071082e-001 -3.458745e-001 -2.398449e-001 -1.000000e-004 +2004 1941 2005 -8.851862e-001 -3.458745e-001 -3.111530e-001 -1.000000e-004 +2005 1941 1942 -8.851864e-001 -3.458807e-001 -3.111457e-001 -1.000000e-004 +2005 1942 2006 -8.576655e-001 -3.458806e-001 -3.804950e-001 -1.000000e-004 +2006 1942 1943 -8.576653e-001 -3.458788e-001 -3.804971e-001 -1.000000e-004 +2006 1943 2007 -8.247237e-001 -3.458787e-001 -4.474356e-001 -1.000000e-004 +2007 1943 1944 -8.247236e-001 -3.458783e-001 -4.474362e-001 -1.000000e-004 +2007 1944 2008 -7.865704e-001 -3.458782e-001 -5.115421e-001 -1.000000e-004 +2008 1944 1945 -7.865688e-001 -3.458729e-001 -5.115481e-001 -1.000000e-004 +2008 1945 2009 -7.434410e-001 -3.458728e-001 -5.724225e-001 -1.000000e-004 +2009 1945 1946 -7.434429e-001 -3.458777e-001 -5.724170e-001 -1.000000e-004 +2009 1946 2010 -6.956105e-001 -3.458777e-001 -6.296782e-001 -1.000000e-004 +2010 1946 1947 -6.956092e-001 -3.458749e-001 -6.296812e-001 -1.000000e-004 +2010 1947 2011 -6.433849e-001 -3.458749e-001 -6.829542e-001 -1.000000e-004 +2011 1947 1948 -6.433854e-001 -3.458757e-001 -6.829533e-001 -1.000000e-004 +2011 1948 2012 -5.870865e-001 -3.458754e-001 -7.319151e-001 -1.000000e-004 +2012 1948 1949 -5.870894e-001 -3.458799e-001 -7.319106e-001 -1.000000e-004 +2012 1949 2013 -5.270857e-001 -3.458797e-001 -7.762396e-001 -1.000000e-004 +2013 1949 1950 -5.270815e-001 -3.458739e-001 -7.762450e-001 -1.000000e-004 +2013 1950 2014 -4.637421e-001 -3.458736e-001 -8.156682e-001 -1.000000e-004 +2014 1950 1951 -4.637450e-001 -3.458773e-001 -8.156650e-001 -1.000000e-004 +2014 1951 2015 -3.974756e-001 -3.458774e-001 -8.499306e-001 -1.000000e-004 +2015 1951 1952 -3.974722e-001 -3.458735e-001 -8.499337e-001 -1.000000e-004 +2015 1952 2016 -3.286902e-001 -3.458734e-001 -8.788255e-001 -1.000000e-004 +2016 1952 1953 -3.286903e-001 -3.458735e-001 -8.788255e-001 -1.000000e-004 +2016 1953 2017 -2.578277e-001 -3.458734e-001 -9.021621e-001 -1.000000e-004 +2017 1953 1954 -2.578299e-001 -3.458755e-001 -9.021607e-001 -1.000000e-004 +2017 1954 2018 -1.853366e-001 -3.458756e-001 -9.197937e-001 -1.000000e-004 +2018 1954 1955 -1.853385e-001 -3.458774e-001 -9.197926e-001 -1.000000e-004 +2018 1955 2019 -1.116707e-001 -3.458774e-001 -9.316107e-001 -1.000000e-004 +2019 1955 1956 -1.116685e-001 -3.458753e-001 -9.316117e-001 -1.000000e-004 +2019 1956 2020 -3.730235e-002 -3.458753e-001 -9.375387e-001 -1.000000e-004 +2020 1956 1957 -3.730346e-002 -3.458763e-001 -9.375383e-001 -1.000000e-004 +2020 1957 2021 3.730233e-002 -3.458763e-001 -9.375383e-001 -1.000000e-004 +2021 1957 1958 3.730347e-002 -3.458753e-001 -9.375387e-001 -1.000000e-004 +2021 1958 2022 1.116708e-001 -3.458753e-001 -9.316115e-001 -1.000000e-004 +2022 1958 1959 1.116684e-001 -3.458774e-001 -9.316110e-001 -1.000000e-004 +2022 1959 2023 1.853365e-001 -3.458774e-001 -9.197930e-001 -1.000000e-004 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6.433847e-001 -3.458758e-001 -6.829540e-001 -1.000000e-004 +2030 1966 1967 6.433856e-001 -3.458749e-001 -6.829535e-001 -1.000000e-004 +2030 1967 2031 6.956113e-001 -3.458748e-001 -6.296789e-001 -1.000000e-004 +2031 1967 1968 6.956084e-001 -3.458776e-001 -6.296805e-001 -1.000000e-004 +2031 1968 347 7.434395e-001 -3.458778e-001 -5.724214e-001 -1.000000e-004 + 347 1968 348 7.434444e-001 -3.458728e-001 -5.724181e-001 -1.000000e-004 + 347 348 137 7.856497e-001 -3.458940e-001 -5.129442e-001 -1.000000e-004 + 137 348 138 7.932299e-001 -3.202400e-001 -5.179119e-001 -1.000000e-004 + 21 20 331 7.992703e-001 -4.293031e-001 4.205542e-001 -1.000000e-004 + 331 20 19 7.811113e-001 -4.160351e-001 4.655962e-001 -1.000000e-004 + 331 19 2032 7.814159e-001 -4.160529e-001 4.650691e-001 -1.000000e-004 +2032 19 330 7.818891e-001 -4.183478e-001 4.622061e-001 -1.000000e-004 +2032 330 2033 7.411229e-001 -4.183902e-001 5.250586e-001 -1.000000e-004 +2033 330 1969 7.411212e-001 -4.183849e-001 5.250652e-001 -1.000000e-004 +2033 1969 2034 6.970613e-001 -4.183850e-001 5.822882e-001 -1.000000e-004 +2034 1969 1970 6.970620e-001 -4.183866e-001 5.822862e-001 -1.000000e-004 +2034 1970 2035 6.485991e-001 -4.183866e-001 6.358238e-001 -1.000000e-004 +2035 1970 1971 6.485981e-001 -4.183847e-001 6.358261e-001 -1.000000e-004 +2035 1971 2036 5.960264e-001 -4.183847e-001 6.853515e-001 -1.000000e-004 +2036 1971 1972 5.960289e-001 -4.183888e-001 6.853469e-001 -1.000000e-004 +2036 1972 2037 5.396975e-001 -4.183889e-001 7.305323e-001 -1.000000e-004 +2037 1972 1973 5.396959e-001 -4.183866e-001 7.305347e-001 -1.000000e-004 +2037 1973 2038 4.799440e-001 -4.183867e-001 7.711072e-001 -1.000000e-004 +2038 1973 1974 4.799430e-001 -4.183853e-001 7.711086e-001 -1.000000e-004 +2038 1974 2039 4.171640e-001 -4.183851e-001 8.068011e-001 -1.000000e-004 +2039 1974 1975 4.171679e-001 -4.183896e-001 8.067968e-001 -1.000000e-004 +2039 1975 2040 3.517475e-001 -4.183898e-001 8.373910e-001 -1.000000e-004 +2040 1975 1976 3.517452e-001 -4.183873e-001 8.373932e-001 -1.000000e-004 +2040 1976 2041 2.841024e-001 -4.183873e-001 8.626923e-001 -1.000000e-004 +2041 1976 1977 2.841014e-001 -4.183862e-001 8.626931e-001 -1.000000e-004 +2041 1977 2042 2.146679e-001 -4.183862e-001 8.825365e-001 -1.000000e-004 +2042 1977 1978 2.146650e-001 -4.183834e-001 8.825385e-001 -1.000000e-004 +2042 1978 2043 1.438687e-001 -4.183834e-001 8.968038e-001 -1.000000e-004 +2043 1978 1979 1.438684e-001 -4.183831e-001 8.968040e-001 -1.000000e-004 +2043 1979 2044 7.215872e-002 -4.183830e-001 9.053998e-001 -1.000000e-004 +2044 1979 1980 7.216281e-002 -4.183866e-001 9.053978e-001 -1.000000e-004 +2044 1980 2045 0.000000e+000 -4.183866e-001 9.082690e-001 -1.000000e-004 +2045 1980 1981 0.000000e+000 -4.183866e-001 9.082690e-001 -1.000000e-004 +2045 1981 2046 -7.215859e-002 -4.183866e-001 9.053981e-001 -1.000000e-004 +2046 1981 1982 -7.216294e-002 -4.183831e-001 9.053994e-001 -1.000000e-004 +2046 1982 2047 -1.438687e-001 -4.183831e-001 8.968040e-001 -1.000000e-004 +2047 1982 1983 -1.438683e-001 -4.183834e-001 8.968039e-001 -1.000000e-004 +2047 1983 2048 -2.146682e-001 -4.183834e-001 8.825378e-001 -1.000000e-004 +2048 1983 1984 -2.146647e-001 -4.183862e-001 8.825373e-001 -1.000000e-004 +2048 1984 2049 -2.841026e-001 -4.183862e-001 8.626927e-001 -1.000000e-004 +2049 1984 1985 -2.841012e-001 -4.183872e-001 8.626926e-001 -1.000000e-004 +2049 1985 2050 -3.517480e-001 -4.183873e-001 8.373921e-001 -1.000000e-004 +2050 1985 1986 -3.517448e-001 -4.183897e-001 8.373922e-001 -1.000000e-004 +2050 1986 2051 -4.171631e-001 -4.183897e-001 8.067992e-001 -1.000000e-004 +2051 1986 1987 -4.171688e-001 -4.183852e-001 8.067986e-001 -1.000000e-004 +2051 1987 2052 -4.799444e-001 -4.183853e-001 7.711077e-001 -1.000000e-004 +2052 1987 1988 -4.799427e-001 -4.183866e-001 7.711081e-001 -1.000000e-004 +2052 1988 2053 -5.396981e-001 -4.183866e-001 7.305331e-001 -1.000000e-004 +2053 1988 1989 -5.396953e-001 -4.183888e-001 7.305339e-001 -1.000000e-004 +2053 1989 2054 -5.960252e-001 -4.183888e-001 6.853501e-001 -1.000000e-004 +2054 1989 1990 -5.960301e-001 -4.183848e-001 6.853483e-001 -1.000000e-004 +2054 1990 2055 -6.485997e-001 -4.183846e-001 6.358244e-001 -1.000000e-004 +2055 1990 1991 -6.485975e-001 -4.183866e-001 6.358254e-001 -1.000000e-004 +2055 1991 2056 -6.970607e-001 -4.183866e-001 5.822877e-001 -1.000000e-004 +2056 1991 1992 -6.970625e-001 -4.183850e-001 5.822867e-001 -1.000000e-004 +2056 1992 2057 -7.411249e-001 -4.183848e-001 5.250600e-001 -1.000000e-004 +2057 1992 1993 -7.411192e-001 -4.183901e-001 5.250638e-001 -1.000000e-004 +2057 1993 2058 -7.804938e-001 -4.183901e-001 4.645203e-001 -1.000000e-004 +2058 1993 1994 -7.804977e-001 -4.183862e-001 4.645172e-001 -1.000000e-004 +2058 1994 2059 -8.149345e-001 -4.183861e-001 4.010421e-001 -1.000000e-004 +2059 1994 1995 -8.149311e-001 -4.183898e-001 4.010452e-001 -1.000000e-004 +2059 1995 2060 -8.442185e-001 -4.183900e-001 3.350298e-001 -1.000000e-004 +2060 1995 1996 -8.442241e-001 -4.183835e-001 3.350237e-001 -1.000000e-004 +2060 1996 2061 -8.681728e-001 -4.183833e-001 2.668920e-001 -1.000000e-004 +2061 1996 1997 -8.681693e-001 -4.183877e-001 2.668965e-001 -1.000000e-004 +2061 1997 2062 -8.866294e-001 -4.183878e-001 1.970785e-001 -1.000000e-004 +2062 1997 1998 -8.866306e-001 -4.183861e-001 1.970767e-001 -1.000000e-004 +2062 1998 2063 -8.994857e-001 -4.183862e-001 1.260099e-001 -1.000000e-004 +2063 1998 1999 -8.994865e-001 -4.183848e-001 1.260084e-001 -1.000000e-004 +2063 1999 2064 -9.066545e-001 -4.183848e-001 5.414622e-002 -1.000000e-004 +2064 1999 2000 -9.066535e-001 -4.183866e-001 5.414836e-002 -1.000000e-004 +2064 2000 2065 -9.080895e-001 -4.183867e-001 -1.805728e-002 -1.000000e-004 +2065 2000 2001 -9.080896e-001 -4.183863e-001 -1.805770e-002 -1.000000e-004 +2065 2001 2066 -9.037840e-001 -4.183863e-001 -9.015174e-002 -1.000000e-004 +2066 2001 2002 -9.037842e-001 -4.183857e-001 -9.015253e-002 -1.000000e-004 +2066 2002 2067 -8.937653e-001 -4.183857e-001 -1.616694e-001 -1.000000e-004 +2067 2002 2003 -8.937647e-001 -4.183882e-001 -1.616662e-001 -1.000000e-004 +2067 2003 2068 -8.780942e-001 -4.183882e-001 -2.321677e-001 -1.000000e-004 +2068 2003 2004 -8.780947e-001 -4.183847e-001 -2.321721e-001 -1.000000e-004 +2068 2004 2069 -8.568743e-001 -4.183847e-001 -3.011986e-001 -1.000000e-004 +2069 2004 2005 -8.568744e-001 -4.183828e-001 -3.012011e-001 -1.000000e-004 +2069 2005 2070 -8.302337e-001 -4.183829e-001 -3.683311e-001 -1.000000e-004 +2070 2005 2006 -8.302340e-001 -4.183874e-001 -3.683252e-001 -1.000000e-004 +2070 2006 2071 -7.983454e-001 -4.183874e-001 -4.331241e-001 -1.000000e-004 +2071 2006 2007 -7.983454e-001 -4.183870e-001 -4.331246e-001 -1.000000e-004 +2071 2007 2072 -7.614106e-001 -4.183871e-001 -4.951830e-001 -1.000000e-004 +2072 2007 2008 -7.614112e-001 -4.183894e-001 -4.951800e-001 -1.000000e-004 +2072 2008 2073 -7.196592e-001 -4.183897e-001 -5.541126e-001 -1.000000e-004 +2073 2008 2009 -7.196595e-001 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-1.741565e-01 9.609290e-01 -1.000000e-04 +1759 1913 1752 9.176346e-01 1.386664e-01 -3.724491e-01 -1.000000e-04 +1913 1759 1914 9.297586e-01 1.182104e-01 -3.486765e-01 -1.000000e-04 +1758 1912 1915 2.964578e-02 -1.848916e-01 9.823117e-01 -1.000000e-04 +1914 1759 1916 9.303083e-01 1.177664e-01 -3.473580e-01 -1.000000e-04 +1760 1915 1917 -1.032483e-01 -1.055993e-01 9.890342e-01 -1.000000e-04 +1915 1760 1758 2.700067e-02 -1.866387e-01 9.820575e-01 -1.000000e-04 +1761 1916 1759 9.062647e-01 8.851499e-02 -4.133394e-01 -1.000000e-04 +1916 1761 1918 9.339717e-01 3.845478e-02 -3.552718e-01 -1.000000e-04 +1918 1761 1762 9.219007e-01 3.512097e-02 -3.858311e-01 -1.000000e-04 +1919 1762 1920 9.185757e-01 2.705519e-02 -3.943180e-01 -1.000000e-04 +1762 1919 1918 9.246385e-01 3.053559e-02 -3.796200e-01 -1.000000e-04 +1917 1763 1760 -1.423381e-01 -1.151809e-01 9.830937e-01 -1.000000e-04 +1763 1917 1921 -2.551123e-01 -2.986111e-02 9.664502e-01 -1.000000e-04 +1921 1764 1763 -2.319103e-01 -1.766581e-02 9.725767e-01 -1.000000e-04 +1920 1765 1766 9.322398e-01 5.408273e-02 -3.577766e-01 -1.000000e-04 +1920 1762 1765 9.236083e-01 4.533518e-02 -3.806473e-01 -1.000000e-04 +1764 1921 1922 -3.093800e-01 -8.185281e-03 9.509033e-01 -1.000000e-04 +1766 1923 1920 9.358089e-01 4.974886e-02 -3.489795e-01 -1.000000e-04 +1923 1766 1767 9.302896e-01 3.721386e-02 -3.649334e-01 -1.000000e-04 +1922 1768 1764 -3.210691e-01 -1.850531e-02 9.468750e-01 -1.000000e-04 +1768 1922 1924 -2.752215e-01 -3.059083e-02 9.608940e-01 -1.000000e-04 +1767 1925 1923 9.510318e-01 9.392080e-03 -3.089502e-01 -1.000000e-04 +1924 1769 1768 -3.145341e-01 -7.685931e-02 9.461295e-01 -1.000000e-04 +1926 1767 1770 9.419530e-01 -5.341573e-02 -3.314683e-01 -1.000000e-04 +1767 1926 1925 9.482587e-01 -9.624171e-04 -3.174974e-01 -1.000000e-04 +1925 1926 1927 9.518502e-01 -8.126396e-03 -3.064558e-01 -1.000000e-04 +1770 1927 1926 9.467614e-01 -5.799903e-02 -3.166684e-01 -1.000000e-04 +1769 1924 1928 -1.735721e-01 -1.075481e-01 9.789311e-01 -1.000000e-04 +1774 1770 1771 -1.160568e-01 -9.697820e-01 2.146011e-01 -1.000000e-04 +1770 1774 1927 9.475865e-01 -5.560766e-02 -3.146229e-01 -1.000000e-04 +1928 1772 1769 -2.091117e-01 -1.424525e-01 9.674604e-01 -1.000000e-04 +1772 1928 1929 -1.846110e-01 -1.533358e-01 9.707764e-01 -1.000000e-04 +1774 1930 1927 9.344390e-01 -3.584548e-02 -3.543147e-01 -1.000000e-04 +1929 1776 1772 -1.888706e-01 -1.540929e-01 9.698367e-01 -1.000000e-04 +1776 1929 1931 -1.899762e-01 -1.539375e-01 9.696455e-01 -1.000000e-04 +1775 1932 1930 9.391645e-01 -6.628290e-02 -3.370113e-01 -1.000000e-04 +1930 1774 1775 9.272205e-01 -4.836506e-02 -3.713799e-01 -1.000000e-04 +1931 1777 1776 -2.093900e-01 -1.827323e-01 9.606064e-01 -1.000000e-04 +1932 1775 1778 9.326476e-01 -7.627275e-02 -3.526344e-01 -1.000000e-04 +1932 1779 1933 9.406537e-01 -1.072099e-01 -3.219886e-01 -1.000000e-04 +1779 1932 1778 9.252248e-01 -7.751920e-02 -3.714160e-01 -1.000000e-04 +1777 1931 1934 -1.794743e-01 -1.886301e-01 9.655090e-01 -1.000000e-04 +1933 1935 1936 9.239402e-01 -1.174134e-01 -3.640722e-01 -1.000000e-04 +1933 1779 1935 9.258509e-01 -1.240421e-01 -3.569506e-01 -1.000000e-04 +1934 1780 1777 -1.896292e-01 -1.998894e-01 9.612934e-01 -1.000000e-04 +1780 1934 1937 -1.301668e-01 -2.283786e-01 9.648315e-01 -1.000000e-04 +1936 1935 1938 9.425416e-01 -5.846603e-02 -3.289331e-01 -1.000000e-04 +1781 1938 1935 9.185596e-01 -1.814842e-01 -3.511578e-01 -1.000000e-04 +1935 1779 1781 9.143450e-01 -1.735614e-01 -3.658548e-01 -1.000000e-04 +1938 1781 1782 8.873280e-01 -2.390834e-01 -3.943197e-01 -1.000000e-04 +1780 1937 1939 -1.065377e-01 -2.211167e-01 9.694107e-01 -1.000000e-04 +1782 1940 1938 8.864797e-01 -2.389243e-01 -3.963193e-01 -1.000000e-04 +1939 1783 1780 -1.102638e-01 -2.260964e-01 9.678441e-01 -1.000000e-04 +1783 1939 1941 -8.986608e-02 -2.296049e-01 9.691262e-01 -1.000000e-04 +1940 1782 1784 8.265440e-01 -3.339936e-01 -4.530709e-01 -1.000000e-04 +1940 1784 1942 8.331318e-01 -3.348175e-01 -4.402144e-01 -1.000000e-04 +1941 1785 1783 -3.875897e-02 -1.497472e-01 9.879643e-01 -1.000000e-04 +1942 1786 1943 8.118395e-01 -3.120399e-01 -4.935056e-01 -1.000000e-04 +1784 1786 1942 8.325214e-01 -3.354840e-01 -4.408612e-01 -1.000000e-04 +1944 1785 1941 -5.120918e-02 -1.463610e-01 9.879049e-01 -1.000000e-04 +1944 1787 1785 -1.040771e-02 -1.354039e-01 9.907358e-01 -1.000000e-04 +1787 1944 1945 -3.401339e-02 -1.211261e-01 9.920542e-01 -1.000000e-04 +1789 1943 1786 7.556999e-01 -3.540341e-01 -5.509787e-01 -1.000000e-04 +1787 1945 1788 -2.674882e-03 -8.652669e-02 9.962459e-01 -1.000000e-04 +1789 1946 1943 6.932815e-01 -3.027603e-01 -6.539855e-01 -1.000000e-04 +1945 1790 1788 -3.856378e-02 -8.714129e-02 9.954493e-01 -1.000000e-04 +1946 1789 1791 6.072256e-01 -3.416920e-01 -7.173030e-01 -1.000000e-04 +1945 1947 1790 -3.795188e-02 -8.742684e-02 9.954477e-01 -1.000000e-04 +1946 1791 1948 5.146344e-01 -2.904335e-01 -8.067216e-01 -1.000000e-04 +1947 1792 1790 -5.670768e-02 -9.877385e-02 9.934928e-01 -1.000000e-04 +1792 1947 1949 -6.396248e-02 -9.745204e-02 9.931827e-01 -1.000000e-04 +1948 1791 1950 4.736640e-01 -3.052626e-01 -8.261096e-01 -1.000000e-04 +1949 1794 1792 -3.868022e-02 -6.522992e-02 9.971203e-01 -1.000000e-04 +1793 1950 1791 5.274394e-01 -2.573570e-01 -8.096759e-01 -1.000000e-04 +1950 1793 1951 3.043301e-01 -2.221646e-01 -9.262970e-01 -1.000000e-04 +1952 1799 1795 -8.833308e-01 -4.660553e-01 -5.019183e-02 -1.000000e-04 +1952 1795 1953 -7.005228e-01 -6.326090e-01 -3.302630e-01 -1.000000e-04 +1796 1953 1795 -7.012490e-01 -6.211825e-01 -3.498316e-01 -1.000000e-04 +1953 1796 1797 -5.876407e-01 -5.944625e-01 -5.489015e-01 -1.000000e-04 +1954 1794 1949 -1.070720e-02 -6.961126e-02 9.975167e-01 -1.000000e-04 +1799 1955 1798 -9.295147e-01 -3.582000e-01 8.772196e-02 -1.000000e-04 +1952 1955 1799 -8.868823e-01 -4.551054e-01 -7.949123e-02 -1.000000e-04 +1956 1953 1797 -4.286290e-01 -6.515968e-01 -6.258584e-01 -1.000000e-04 +1801 1957 1802 -9.131778e-01 -4.016909e-01 6.892601e-02 -1.000000e-04 +1957 1801 1798 -9.125948e-01 -4.002605e-01 8.344070e-02 -1.000000e-04 +1957 1798 1955 -9.223612e-01 -3.648614e-01 1.269884e-01 -1.000000e-04 +1797 1800 1956 -3.376434e-01 -5.780093e-01 -7.429012e-01 -1.000000e-04 +1954 1804 1794 -2.312233e-02 -7.588590e-02 9.968484e-01 -1.000000e-04 +1804 1954 1958 -4.333908e-02 -6.606854e-02 9.968734e-01 -1.000000e-04 +1805 1951 1793 -1.288085e-01 -5.892470e-01 -7.976192e-01 -1.000000e-04 +1806 1802 1959 -8.715569e-01 -4.766478e-01 1.148716e-01 -1.000000e-04 +1959 1802 1957 -8.788676e-01 -4.405668e-01 1.830098e-01 -1.000000e-04 +1960 1956 1800 -2.010139e-01 -6.173448e-01 -7.605780e-01 -1.000000e-04 +1804 1958 1807 -7.684695e-02 -1.047780e-01 9.915221e-01 -1.000000e-04 +1951 1805 1961 9.247886e-02 -6.950032e-01 -7.130345e-01 -1.000000e-04 +1806 1959 1962 -8.336216e-01 -5.115382e-01 2.083357e-01 -1.000000e-04 +1808 1961 1805 -2.367811e-01 -7.314835e-01 -6.394268e-01 -1.000000e-04 +1806 1962 1809 -8.370039e-01 -4.421792e-01 3.223385e-01 -1.000000e-04 +1800 1810 1960 -3.027689e-02 -4.877444e-01 -8.724613e-01 -1.000000e-04 +1807 1958 1963 -1.515994e-01 -8.915179e-02 9.844133e-01 -1.000000e-04 +1961 1808 1964 -3.362694e-01 -6.688162e-01 -6.630292e-01 -1.000000e-04 +1965 1809 1962 -8.329103e-01 -4.440032e-01 3.303356e-01 -1.000000e-04 +1960 1810 1966 -3.567027e-02 -4.860232e-01 -8.732177e-01 -1.000000e-04 +1963 1812 1807 -3.333898e-01 -2.724478e-01 9.025649e-01 -1.000000e-04 +1808 1813 1964 -2.778408e-01 -6.551609e-01 -7.025444e-01 -1.000000e-04 +1809 1965 1811 -7.997369e-01 -3.874924e-01 4.585526e-01 -1.000000e-04 +1966 1810 1814 1.506150e-01 -3.245403e-01 -9.338034e-01 -1.000000e-04 +1967 1811 1965 -8.180114e-01 -3.770503e-01 4.343852e-01 -1.000000e-04 +1968 1812 1963 -4.357616e-01 -2.478491e-01 8.652645e-01 -1.000000e-04 +1815 1964 1813 -2.106264e-01 -6.818872e-01 -7.004758e-01 -1.000000e-04 +1964 1815 1969 -2.527123e-01 -6.423884e-01 -7.235148e-01 -1.000000e-04 +1811 1967 1816 -7.847412e-01 -2.393550e-01 5.717433e-01 -1.000000e-04 +1966 1814 1817 1.942790e-01 -3.274251e-01 -9.246883e-01 -1.000000e-04 +1966 1817 1970 1.093215e-01 -2.932054e-01 -9.497786e-01 -1.000000e-04 +1970 1817 1819 2.306925e-01 -1.925488e-01 -9.537850e-01 -1.000000e-04 +1812 1968 1818 -5.964349e-01 -6.282834e-01 4.995251e-01 -1.000000e-04 +1821 1969 1815 2.853606e-02 -6.079041e-01 -7.934975e-01 -1.000000e-04 +1816 1971 1822 -6.820381e-01 -1.658711e-01 7.122575e-01 -1.000000e-04 +1971 1816 1967 -7.371132e-01 -2.601873e-01 6.236719e-01 -1.000000e-04 +1972 1820 1818 -6.660102e-01 -7.058918e-01 2.411373e-01 -1.000000e-04 +1972 1818 1968 -6.905882e-01 -6.072399e-01 3.928710e-01 -1.000000e-04 +1969 1821 1973 -2.166526e-02 -5.822029e-01 -8.127548e-01 -1.000000e-04 +1822 1974 1824 -6.459668e-01 -1.305338e-01 7.521222e-01 -1.000000e-04 +1974 1822 1971 -6.699926e-01 -1.648107e-01 7.238421e-01 -1.000000e-04 +1970 1819 1975 1.930390e-01 -1.923627e-01 -9.621500e-01 -1.000000e-04 +1823 1973 1821 2.594931e-01 -3.572875e-01 -8.972229e-01 -1.000000e-04 +1826 1975 1819 2.226903e-01 -1.494364e-01 -9.633679e-01 -1.000000e-04 +1825 1820 1976 -6.931213e-01 -6.393146e-01 3.329559e-01 -1.000000e-04 +1976 1820 1972 -6.696153e-01 -7.038919e-01 2.369631e-01 -1.000000e-04 +1827 1973 1823 3.904128e-01 -3.442329e-01 -8.538627e-01 -1.000000e-04 +1824 1974 1977 -6.006729e-01 -1.205089e-01 7.903604e-01 -1.000000e-04 +1975 1826 1978 1.030909e-01 -1.422576e-01 -9.844466e-01 -1.000000e-04 +1829 1978 1826 1.590601e-01 -5.117425e-02 -9.859417e-01 -1.000000e-04 +1973 1827 1979 2.739990e-01 -2.491383e-01 -9.288997e-01 -1.000000e-04 +1977 1828 1824 -5.354158e-01 -1.151290e-02 8.445102e-01 -1.000000e-04 +1830 1825 1980 -6.685371e-01 -4.901190e-01 5.593223e-01 -1.000000e-04 +1976 1980 1825 -6.642797e-01 -6.313200e-01 4.002094e-01 -1.000000e-04 +1828 1977 1981 -5.081210e-01 -1.364028e-02 8.611777e-01 -1.000000e-04 +1831 1979 1827 4.190040e-01 -1.590411e-01 -8.939472e-01 -1.000000e-04 +1979 1831 1982 1.842761e-01 -5.597427e-02 -9.812794e-01 -1.000000e-04 +1981 1832 1828 -3.805691e-01 1.065177e-01 9.185974e-01 -1.000000e-04 +1833 1978 1829 1.174699e-01 -7.067258e-02 -9.905585e-01 -1.000000e-04 +1830 1983 1834 -5.255372e-01 -2.486417e-01 8.136265e-01 -1.000000e-04 +1983 1830 1980 -5.973561e-01 -4.795973e-01 6.427691e-01 -1.000000e-04 +1832 1981 1984 -4.104089e-01 1.106766e-01 9.051603e-01 -1.000000e-04 +1835 1982 1831 4.171364e-01 9.720177e-02 -9.036310e-01 -1.000000e-04 +1982 1835 1985 1.462306e-01 1.844547e-01 -9.719018e-01 -1.000000e-04 +1984 1836 1832 -2.786397e-01 2.503112e-01 9.272024e-01 -1.000000e-04 +1978 1833 1986 9.300132e-02 -5.424611e-02 -9.941872e-01 -1.000000e-04 +1983 1837 1834 -3.364102e-01 -2.330185e-01 9.124311e-01 -1.000000e-04 +1837 1983 1987 -5.031731e-01 -8.116794e-02 8.603654e-01 -1.000000e-04 +1986 1838 1988 1.184238e-01 1.643732e-02 -9.928271e-01 -1.000000e-04 +1838 1986 1833 1.732054e-01 8.584642e-03 -9.848483e-01 -1.000000e-04 +1839 1985 1835 3.755365e-01 3.002221e-01 -8.768347e-01 -1.000000e-04 +1836 1984 1989 -2.738420e-01 2.481868e-01 9.292007e-01 -1.000000e-04 +1840 1988 1838 1.541748e-01 2.978834e-02 -9.875944e-01 -1.000000e-04 +1985 1839 1990 2.725343e-01 3.231915e-01 -9.062407e-01 -1.000000e-04 +1985 1990 1991 1.181278e-01 4.807424e-01 -8.688686e-01 -1.000000e-04 +1987 1841 1837 -2.401609e-01 7.409047e-02 9.679015e-01 -1.000000e-04 +1842 1990 1839 2.179879e-01 2.580551e-01 -9.412167e-01 -1.000000e-04 +1990 1992 1991 5.209371e-02 4.693452e-01 -8.814768e-01 -1.000000e-04 +1988 1840 1993 1.712069e-01 2.027620e-02 -9.850264e-01 -1.000000e-04 +1842 1992 1990 4.170120e-02 4.480201e-01 -8.930504e-01 -1.000000e-04 +1989 1843 1836 -2.748169e-01 2.474973e-01 9.290967e-01 -1.000000e-04 +1844 1993 1840 1.089463e-01 -2.127279e-02 -9.938200e-01 -1.000000e-04 +1994 1841 1987 -4.099764e-01 1.720475e-01 8.957226e-01 -1.000000e-04 +1841 1994 1845 -1.635421e-01 3.609717e-01 9.181249e-01 -1.000000e-04 +1843 1989 1995 -2.322852e-01 2.189452e-01 9.476849e-01 -1.000000e-04 +1993 1844 1996 1.647157e-01 -4.186876e-02 -9.854521e-01 -1.000000e-04 +1845 1994 1997 -2.955487e-01 3.769403e-01 8.778194e-01 -1.000000e-04 +1842 1998 1992 7.822987e-02 4.556188e-01 -8.867308e-01 -1.000000e-04 +1999 1992 1998 -2.518818e-02 5.220915e-01 -8.525174e-01 -1.000000e-04 +1846 1996 1844 -4.599466e-02 -1.314782e-01 -9.902515e-01 -1.000000e-04 +1847 1845 1997 -1.134046e-01 4.673980e-01 8.767431e-01 -1.000000e-04 +1998 1842 1849 -1.149705e-02 3.376677e-01 -9.411952e-01 -1.000000e-04 +1849 1999 1998 -1.233668e-01 3.987500e-01 -9.087239e-01 -1.000000e-04 +1843 1995 1848 -5.889664e-01 -8.413040e-02 8.037665e-01 -1.000000e-04 +1996 1846 2000 8.201553e-02 -1.781186e-01 -9.805851e-01 -1.000000e-04 +1997 2001 1847 -2.302412e-01 5.246549e-01 8.195890e-01 -1.000000e-04 +1850 1999 1849 -1.400791e-01 3.933795e-01 -9.086421e-01 -1.000000e-04 +2002 1999 1850 -3.730059e-02 3.344442e-01 -9.416771e-01 -1.000000e-04 +1848 2003 1851 -7.444713e-01 -3.409954e-01 5.740075e-01 -1.000000e-04 +2003 1848 1995 -6.446326e-01 -7.928133e-02 7.603705e-01 -1.000000e-04 +2000 1846 1852 -1.412272e-01 -4.081778e-01 -9.019123e-01 -1.000000e-04 +1853 1847 2001 -2.603384e-01 5.082327e-01 8.209284e-01 -1.000000e-04 +1853 2001 2004 -3.432061e-01 5.354544e-01 7.716853e-01 -1.000000e-04 +2002 1850 2005 -9.176606e-02 3.100698e-01 -9.462746e-01 -1.000000e-04 +2006 1851 2003 -8.227096e-01 -3.063895e-01 4.788260e-01 -1.000000e-04 +2000 1852 2007 -2.259481e-01 -3.857126e-01 -8.945241e-01 -1.000000e-04 +2007 1852 1854 -3.020537e-01 -4.614758e-01 -8.341484e-01 -1.000000e-04 +1855 2005 1850 -4.112553e-01 -7.827268e-02 -9.081533e-01 -1.000000e-04 +1851 2006 1856 -8.405365e-01 -3.701364e-01 3.955976e-01 -1.000000e-04 +2004 1857 1853 -5.799678e-01 3.295235e-01 7.450178e-01 -1.000000e-04 +2005 1855 2008 -3.465957e-01 -1.007349e-01 -9.325899e-01 -1.000000e-04 +2009 1856 2006 -9.100818e-01 -3.203150e-01 2.629628e-01 -1.000000e-04 +1854 2010 2007 -3.822509e-01 -4.462947e-01 -8.091386e-01 -1.000000e-04 +1854 1858 2010 -3.652568e-01 -4.262605e-01 -8.275805e-01 -1.000000e-04 +1859 2008 1855 -6.251685e-01 -3.964197e-01 -6.723212e-01 -1.000000e-04 +1861 2009 2011 -9.412240e-01 -3.095730e-01 1.351364e-01 -1.000000e-04 +1856 2009 1861 -9.168157e-01 -3.379244e-01 2.127347e-01 -1.000000e-04 +2012 1858 1862 -3.938558e-01 -4.639473e-01 -7.934926e-01 -1.000000e-04 +1858 2012 2010 -3.526336e-01 -4.268760e-01 -8.327223e-01 -1.000000e-04 +1857 2004 2013 -6.651128e-01 3.353371e-01 6.672136e-01 -1.000000e-04 +1857 2013 1863 -8.334231e-01 5.499789e-02 5.498919e-01 -1.000000e-04 +2008 1859 2014 -6.503503e-01 -3.859699e-01 -6.542719e-01 -1.000000e-04 +1860 2014 1859 -6.805785e-01 -4.361918e-01 -5.886847e-01 -1.000000e-04 +1865 2011 1866 -9.417877e-01 -3.152974e-01 1.167196e-01 -1.000000e-04 +1861 2011 1865 -9.400762e-01 -3.156930e-01 1.288199e-01 -1.000000e-04 +1862 2015 2012 -3.883755e-01 -4.665771e-01 -7.946510e-01 -1.000000e-04 +2014 1860 2016 -6.998779e-01 -4.362242e-01 -5.655789e-01 -1.000000e-04 +1864 2016 1860 -7.022854e-01 -4.442669e-01 -5.562573e-01 -1.000000e-04 +1864 2017 2016 -6.753731e-01 -4.533617e-01 -5.816652e-01 -1.000000e-04 +1866 2011 2018 -9.350916e-01 -3.281883e-01 1.337764e-01 -1.000000e-04 +1863 2013 2019 -8.888625e-01 9.323759e-02 4.485870e-01 -1.000000e-04 +1867 2017 1864 -7.193718e-01 -5.073457e-01 -4.744519e-01 -1.000000e-04 +2017 1867 2020 -7.466614e-01 -4.881604e-01 -4.518807e-01 -1.000000e-04 +1868 2020 1867 -7.642334e-01 -5.274267e-01 -3.711716e-01 -1.000000e-04 +1869 2021 1868 -8.393041e-01 -4.451423e-01 -3.121167e-01 -1.000000e-04 +2021 1869 2022 -9.064937e-01 -3.904839e-01 -1.605974e-01 -1.000000e-04 +1866 2022 1869 -9.026169e-01 -4.201358e-01 -9.364083e-02 -1.000000e-04 +2022 1866 2018 -9.391165e-01 -3.415423e-01 3.753692e-02 -1.000000e-04 +1862 2023 2015 -5.021187e-01 -4.819034e-01 -7.180849e-01 -1.000000e-04 +2023 1862 1870 -5.194831e-01 -5.268109e-01 -6.727612e-01 -1.000000e-04 +2020 1868 2021 -8.446433e-01 -4.477333e-01 -2.934497e-01 -1.000000e-04 +1870 2024 2023 -5.540423e-01 -5.157435e-01 -6.534874e-01 -1.000000e-04 +1871 2024 1870 -5.516911e-01 -5.141828e-01 -6.566986e-01 -1.000000e-04 +2025 1873 1872 -9.744346e-01 -1.960700e-01 1.096986e-01 -1.000000e-04 +2019 1872 1863 -9.618416e-01 -9.040239e-02 2.582406e-01 -1.000000e-04 +1872 2019 2025 -9.681386e-01 -8.053885e-02 2.371099e-01 -1.000000e-04 +1871 2026 2024 -5.941301e-01 -4.832120e-01 -6.430518e-01 -1.000000e-04 +2025 1874 1873 -9.742871e-01 -2.151066e-01 -6.703551e-02 -1.000000e-04 +2026 1871 1875 -6.054502e-01 -4.886404e-01 -6.282202e-01 -1.000000e-04 +2026 1876 2027 -7.038793e-01 -4.433465e-01 -5.549755e-01 -1.000000e-04 +1876 2026 1875 -6.598697e-01 -4.731433e-01 -5.837015e-01 -1.000000e-04 +1877 2027 1876 -7.525368e-01 -4.702017e-01 -4.610843e-01 -1.000000e-04 +1877 1878 2028 -8.802370e-01 -4.239201e-01 -2.132478e-01 -1.000000e-04 +1879 2028 1878 -8.827349e-01 -4.206419e-01 -2.093790e-01 -1.000000e-04 +2028 1879 2029 -9.241007e-01 -3.489262e-01 -1.558475e-01 -1.000000e-04 +1874 2029 1879 -9.198875e-01 -3.408179e-01 -1.940363e-01 -1.000000e-04 +2029 1874 2030 -9.578270e-01 -2.604536e-01 -1.213729e-01 -1.000000e-04 +1874 2025 2030 -9.678021e-01 -2.492222e-01 -3.531968e-02 -1.000000e-04 +2027 1877 2031 -8.183278e-01 -3.971546e-01 -4.154610e-01 -1.000000e-04 +2031 1877 2028 -8.769741e-01 -3.662641e-01 -3.110740e-01 -1.000000e-04 +2032 1880 2033 9.872848e-01 1.587493e-01 8.204350e-03 -1.000000e-04 +2032 1881 1880 9.249863e-01 -1.286884e-01 3.575466e-01 -1.000000e-04 +1881 2032 2034 8.454109e-01 -2.004855e-02 5.337400e-01 -1.000000e-04 +1885 2033 1880 9.919667e-01 1.192520e-01 -4.220299e-02 -1.000000e-04 +1882 2035 1884 7.568541e-01 -7.336445e-02 6.494533e-01 -1.000000e-04 +2035 1882 2034 7.418455e-01 -9.870268e-02 6.632670e-01 -1.000000e-04 +2034 1882 1881 7.959931e-01 -9.959001e-02 5.970568e-01 -1.000000e-04 +2036 2037 2038 9.665293e-01 -6.655006e-02 2.477746e-01 -1.000000e-04 +1888 2038 2039 9.414655e-01 -1.808171e-01 2.845134e-01 -1.000000e-04 +2039 1890 1888 9.113444e-01 -1.842827e-01 3.680913e-01 -1.000000e-04 +1890 2039 2040 9.056198e-01 -1.636919e-01 3.912259e-01 -1.000000e-04 +1885 2041 2033 9.110589e-01 2.940115e-01 -2.890136e-01 -1.000000e-04 +2035 2042 1884 7.292228e-01 -6.235060e-02 6.814298e-01 -1.000000e-04 +2037 1887 1886 9.906257e-01 -3.497644e-02 1.320507e-01 -1.000000e-04 +2037 1886 2043 9.936727e-01 -1.371853e-02 1.114739e-01 -1.000000e-04 +1887 2037 2036 9.616070e-01 -2.999929e-02 2.727857e-01 -1.000000e-04 +2036 1893 1887 9.448877e-01 -8.716454e-02 3.155780e-01 -1.000000e-04 +1893 2036 2038 9.523501e-01 -1.139920e-01 2.829046e-01 -1.000000e-04 +2038 1888 1893 9.338407e-01 -1.223684e-01 3.361065e-01 -1.000000e-04 +1894 1890 2040 8.339712e-01 -2.273672e-01 5.027884e-01 -1.000000e-04 +1894 2044 1895 7.216403e-01 -2.166067e-01 6.575081e-01 -1.000000e-04 +2044 1894 2040 7.781478e-01 -1.810785e-01 6.014121e-01 -1.000000e-04 +2044 2045 1895 6.846914e-01 -1.596996e-01 7.111214e-01 -1.000000e-04 +1891 1884 2042 7.307976e-01 -6.001052e-02 6.799512e-01 -1.000000e-04 +2042 2046 1891 7.398405e-01 -5.785383e-02 6.702902e-01 -1.000000e-04 +2043 1886 1892 9.957091e-01 -9.148712e-02 -1.390977e-02 -1.000000e-04 +2047 2041 1896 8.566110e-01 3.270908e-01 -3.990353e-01 -1.000000e-04 +1885 1896 2041 9.016974e-01 2.782847e-01 -3.309069e-01 -1.000000e-04 +1898 1891 2046 6.825819e-01 -1.441336e-01 7.164548e-01 -1.000000e-04 +1892 2048 2043 9.940159e-01 -1.090927e-01 5.585210e-03 -1.000000e-04 +2045 2049 1895 4.945998e-01 -1.924008e-01 8.475571e-01 -1.000000e-04 +1897 2050 1896 8.529937e-01 3.196323e-01 -4.125978e-01 -1.000000e-04 +1896 2050 2047 8.541528e-01 3.249106e-01 -4.060248e-01 -1.000000e-04 +2046 1900 1898 6.628175e-01 -1.437740e-01 7.348483e-01 -1.000000e-04 +1900 2046 2051 7.022229e-01 -1.768690e-01 6.896378e-01 -1.000000e-04 +1899 1900 2051 6.539738e-01 -2.195342e-01 7.239634e-01 -1.000000e-04 +1901 2052 2048 9.925067e-01 -1.172672e-01 -3.433559e-02 -1.000000e-04 +2048 1892 1901 9.917897e-01 -1.252309e-01 -2.589158e-02 -1.000000e-04 +1904 1895 2049 4.931922e-01 -1.941266e-01 8.479837e-01 -1.000000e-04 +2053 2050 1902 9.027652e-01 2.632967e-01 -3.401320e-01 -1.000000e-04 +1897 1902 2050 8.591282e-01 3.206912e-01 -3.988182e-01 -1.000000e-04 +1903 1899 2051 7.116704e-01 -1.986596e-01 6.738394e-01 -1.000000e-04 +2051 2054 1903 7.125230e-01 -1.994896e-01 6.726923e-01 -1.000000e-04 +2055 1909 2056 9.964553e-01 -2.458198e-02 8.045254e-02 -1.000000e-04 +2055 2052 1909 9.991481e-01 -3.913745e-02 -1.308814e-02 -1.000000e-04 +1901 1909 2052 9.942239e-01 -9.138182e-02 5.628723e-02 -1.000000e-04 +2057 1904 2049 2.507954e-01 -7.524350e-02 9.651114e-01 -1.000000e-04 +2054 1905 1903 8.253410e-01 -1.310954e-01 5.492051e-01 -1.000000e-04 +1905 2054 2058 8.334132e-01 -1.485097e-01 5.323225e-01 -1.000000e-04 +2058 1910 1905 8.979105e-01 -1.317109e-01 4.200106e-01 -1.000000e-04 +2058 1911 1910 9.275860e-01 -1.745843e-01 3.303098e-01 -1.000000e-04 +1911 2058 2059 8.979224e-01 -5.096875e-02 4.371928e-01 -1.000000e-04 +2059 1907 1911 9.504590e-01 -6.552304e-02 3.038657e-01 -1.000000e-04 +1907 2059 2060 9.019344e-01 2.420390e-02 4.311943e-01 -1.000000e-04 +2060 1906 1907 9.627567e-01 2.979391e-02 2.687226e-01 -1.000000e-04 +1906 2060 2061 9.307341e-01 1.069278e-01 3.497147e-01 -1.000000e-04 +2061 1908 1906 9.594787e-01 1.251894e-01 2.524445e-01 -1.000000e-04 +1908 2061 2056 9.732590e-01 8.454951e-02 2.135845e-01 -1.000000e-04 +2056 1909 1908 9.767180e-01 8.274596e-02 1.979269e-01 -1.000000e-04 +2053 1902 2062 9.081976e-01 2.624853e-01 -3.260040e-01 -1.000000e-04 +2057 1912 1904 1.735992e-01 -1.422316e-01 9.744914e-01 -1.000000e-04 +1913 2062 1902 9.035821e-01 2.360474e-01 -3.575207e-01 -1.000000e-04 +2062 1913 2063 9.165722e-01 2.263561e-01 -3.296337e-01 -1.000000e-04 +1912 2057 2064 -1.057300e-01 -2.156435e-02 9.941610e-01 -1.000000e-04 +1914 2063 1913 9.085696e-01 2.207178e-01 -3.546617e-01 -1.000000e-04 +2063 1914 2065 9.195705e-01 2.127663e-01 -3.303341e-01 -1.000000e-04 +2064 1915 1912 -1.358590e-02 8.171062e-02 9.965635e-01 -1.000000e-04 +1916 2065 1914 9.172331e-01 1.865388e-01 -3.519755e-01 -1.000000e-04 +2064 1917 1915 -1.272505e-01 3.697985e-02 9.911810e-01 -1.000000e-04 +1918 2065 1916 9.124967e-01 1.801908e-01 -3.672616e-01 -1.000000e-04 +2065 1918 2066 9.224493e-01 1.684313e-01 -3.474452e-01 -1.000000e-04 +1917 2064 2067 -2.710465e-01 1.149023e-01 9.556837e-01 -1.000000e-04 +1920 2068 1919 9.052692e-01 1.289431e-01 -4.047980e-01 -1.000000e-04 +1919 2066 1918 9.096597e-01 1.419943e-01 -3.903292e-01 -1.000000e-04 +2066 1919 2068 9.151861e-01 1.372953e-01 -3.789254e-01 -1.000000e-04 +2067 1921 1917 -2.759663e-01 1.099022e-01 9.548634e-01 -1.000000e-04 +2068 1920 2069 9.225152e-01 1.093095e-01 -3.701582e-01 -1.000000e-04 +1921 2067 2070 -2.491664e-01 9.820802e-02 9.634684e-01 -1.000000e-04 +2070 1922 1921 -3.181055e-01 4.981645e-02 9.467456e-01 -1.000000e-04 +1923 2069 1920 9.272630e-01 1.155328e-01 -3.561396e-01 -1.000000e-04 +2069 1923 2071 9.343770e-01 1.041168e-01 -3.407335e-01 -1.000000e-04 +1922 2070 2072 -1.832333e-01 1.830110e-02 9.828991e-01 -1.000000e-04 +1922 2072 1924 -2.693121e-01 -6.459723e-02 9.608841e-01 -1.000000e-04 +1925 2071 1923 9.395373e-01 1.160144e-01 -3.221961e-01 -1.000000e-04 +2071 1925 2073 9.542509e-01 8.551464e-02 -2.865178e-01 -1.000000e-04 +2073 1925 2074 9.564046e-01 8.740789e-02 -2.786575e-01 -1.000000e-04 +1924 2072 2075 -1.668298e-01 -1.019581e-01 9.806999e-01 -1.000000e-04 +1927 2074 1925 9.485528e-01 4.181405e-02 -3.138457e-01 -1.000000e-04 +2075 1928 1924 -1.730732e-01 -1.102104e-01 9.787233e-01 -1.000000e-04 +2074 1927 2076 9.476204e-01 4.270287e-02 -3.165313e-01 -1.000000e-04 +1928 2075 2077 -1.824039e-01 -1.103910e-01 9.770070e-01 -1.000000e-04 +2077 2078 1928 -1.477760e-01 -9.090671e-02 9.848341e-01 -1.000000e-04 +1928 2078 1929 -1.866119e-01 -1.432513e-01 9.719337e-01 -1.000000e-04 +2076 1930 2079 9.322128e-01 5.334711e-03 -3.618712e-01 -1.000000e-04 +1930 2076 1927 9.324499e-01 5.083916e-03 -3.612636e-01 -1.000000e-04 +2078 1931 1929 -1.916613e-01 -1.455193e-01 9.706133e-01 -1.000000e-04 +1932 2079 1930 9.361142e-01 1.334610e-02 -3.514430e-01 -1.000000e-04 +2079 1932 2080 9.348037e-01 1.481768e-02 -3.548556e-01 -1.000000e-04 +1931 2078 2081 -1.750465e-01 -1.577988e-01 9.718324e-01 -1.000000e-04 +2080 1932 1933 9.374441e-01 2.325901e-02 -3.473581e-01 -1.000000e-04 +1931 2081 2082 -1.697910e-01 -1.557794e-01 9.730898e-01 -1.000000e-04 +1933 2083 2080 9.387267e-01 2.262813e-02 -3.439189e-01 -1.000000e-04 +1931 2082 1934 -1.826105e-01 -1.735573e-01 9.677455e-01 -1.000000e-04 +2083 1933 1936 9.230470e-01 -2.779159e-02 -3.836820e-01 -1.000000e-04 +2082 1937 1934 -1.413063e-01 -1.745211e-01 9.744613e-01 -1.000000e-04 +1937 2082 2084 -1.507243e-01 -1.677302e-01 9.742427e-01 -1.000000e-04 +1936 2085 2083 9.397435e-01 -3.968412e-02 -3.395693e-01 -1.000000e-04 +2085 1936 1938 9.418488e-01 -3.194554e-02 -3.345150e-01 -1.000000e-04 +2084 1939 1937 -1.191054e-01 -1.586197e-01 9.801294e-01 -1.000000e-04 +1939 2084 2086 -1.412653e-01 -1.484453e-01 9.787789e-01 -1.000000e-04 +1940 2087 2085 8.817549e-01 -7.817851e-02 -4.651842e-01 -1.000000e-04 +2085 1938 1940 8.943441e-01 -9.457790e-02 -4.372683e-01 -1.000000e-04 +2086 1941 1939 -1.103836e-01 -1.257522e-01 9.859015e-01 -1.000000e-04 +2086 2088 1941 -1.026525e-01 -1.308908e-01 9.860680e-01 -1.000000e-04 +2087 1942 2089 8.138005e-01 -8.548916e-02 -5.748220e-01 -1.000000e-04 +1942 2087 1940 8.494627e-01 -1.075668e-01 -5.165680e-01 -1.000000e-04 +1941 2088 1944 -5.225506e-02 -1.407317e-01 9.886678e-01 -1.000000e-04 +2090 1944 2088 -1.043929e-01 -1.066213e-01 9.888043e-01 -1.000000e-04 +1943 2089 1942 8.172697e-01 -7.977491e-02 -5.707068e-01 -1.000000e-04 +2090 2091 1944 -5.869224e-02 -9.853206e-02 9.934016e-01 -1.000000e-04 +2089 1943 2092 7.051002e-01 -4.161140e-02 -7.078857e-01 -1.000000e-04 +2091 1945 1944 -4.300389e-02 -7.126506e-02 9.965300e-01 -1.000000e-04 +1946 2092 1943 6.777657e-01 -6.957433e-02 -7.319789e-01 -1.000000e-04 +2092 1946 2093 5.475021e-01 -2.165190e-02 -8.365242e-01 -1.000000e-04 +2094 1945 2091 -7.843504e-02 -6.148127e-02 9.950216e-01 -1.000000e-04 +1947 2094 2095 -8.757485e-02 -2.300735e-02 9.958922e-01 -1.000000e-04 +2094 1947 1945 -4.813689e-02 -3.031753e-02 9.983805e-01 -1.000000e-04 +1948 2093 1946 4.784426e-01 -5.095864e-02 -8.766390e-01 -1.000000e-04 +2093 1948 2096 3.806897e-01 -2.634057e-03 -9.246991e-01 -1.000000e-04 +2095 1949 1947 -7.860866e-02 -1.594571e-02 9.967780e-01 -1.000000e-04 +1950 2096 1948 4.230760e-01 2.238949e-02 -9.058175e-01 -1.000000e-04 +2096 1950 2097 3.362517e-01 1.577211e-02 -9.416401e-01 -1.000000e-04 +2098 1949 2095 -1.203016e-01 4.717964e-03 9.927262e-01 -1.000000e-04 +1951 2097 1950 2.840110e-01 -2.379935e-02 -9.585256e-01 -1.000000e-04 +1952 1953 2099 -6.911136e-01 -6.448360e-01 -3.264177e-01 -1.000000e-04 +2098 1954 1949 -3.041847e-02 4.311699e-02 9.986069e-01 -1.000000e-04 +2097 1951 2100 2.659684e-01 -1.482774e-02 -9.638677e-01 -1.000000e-04 +1955 1952 2101 -7.802677e-01 -6.221416e-01 -6.420410e-02 -1.000000e-04 +2101 1952 2102 -6.927842e-01 -6.968578e-01 -1.855784e-01 -1.000000e-04 +2099 2102 1952 -6.717132e-01 -6.808426e-01 -2.919840e-01 -1.000000e-04 +1954 2098 2103 -1.185250e-01 6.244977e-02 9.909853e-01 -1.000000e-04 +2104 1955 2101 -7.769228e-01 -6.272052e-01 5.481486e-02 -1.000000e-04 +1955 2104 1957 -8.059540e-01 -5.783004e-01 1.265176e-01 -1.000000e-04 +2102 2099 2105 -5.706734e-01 -7.371502e-01 -3.618584e-01 -1.000000e-04 +2105 2099 2106 -4.781109e-01 -6.789569e-01 -5.571602e-01 -1.000000e-04 +2106 2099 1953 -4.582259e-01 -7.819736e-01 -4.225474e-01 -1.000000e-04 +2106 1953 1956 -3.920947e-01 -7.066272e-01 -5.890159e-01 -1.000000e-04 +2103 1958 1954 -7.055167e-02 9.085082e-02 9.933623e-01 -1.000000e-04 +1958 2103 2107 -1.021384e-01 1.165898e-01 9.879143e-01 -1.000000e-04 +1951 1961 2100 7.386722e-02 -1.242894e-01 -9.894927e-01 -1.000000e-04 +2108 1957 2104 -7.997833e-01 -5.793560e-01 1.571413e-01 -1.000000e-04 +1957 2108 1959 -8.036734e-01 -5.674097e-01 1.793189e-01 -1.000000e-04 +2109 2106 1956 -2.934533e-01 -7.098268e-01 -6.403367e-01 -1.000000e-04 +2109 1956 1960 -1.990009e-01 -6.222954e-01 -7.570648e-01 -1.000000e-04 +2100 1961 2110 -3.077018e-02 -8.372718e-02 -9.960135e-01 -1.000000e-04 +1959 2111 1962 -7.972490e-01 -5.675423e-01 2.056449e-01 -1.000000e-04 +2108 2111 1959 -7.971665e-01 -5.705990e-01 1.973381e-01 -1.000000e-04 +2107 1963 1958 -1.834121e-01 9.875122e-02 9.780635e-01 -1.000000e-04 +1963 2107 2112 -5.628061e-02 4.742835e-03 9.984037e-01 -1.000000e-04 +1964 2110 1961 -3.784206e-01 -2.790291e-01 -8.825761e-01 -1.000000e-04 +2113 2109 1960 -1.654264e-01 -6.242262e-01 -7.635285e-01 -1.000000e-04 +1960 1966 2113 -2.337504e-02 -5.418824e-01 -8.401292e-01 -1.000000e-04 +1963 2112 2114 -2.435439e-01 4.457653e-02 9.688649e-01 -1.000000e-04 +1962 2115 1965 -8.067598e-01 -4.925103e-01 3.264541e-01 -1.000000e-04 +2115 1962 2116 -7.943447e-01 -5.651581e-01 2.227396e-01 -1.000000e-04 +2116 1962 2111 -7.955601e-01 -5.688826e-01 2.084627e-01 -1.000000e-04 +2113 1966 2117 -6.440856e-02 -5.272255e-01 -8.472808e-01 -1.000000e-04 +2110 1964 2118 -2.244580e-01 -4.023394e-01 -8.875481e-01 -1.000000e-04 +2119 1965 2115 -8.175439e-01 -5.013446e-01 2.833294e-01 -1.000000e-04 +1965 2119 1967 -8.112411e-01 -3.927811e-01 4.331408e-01 -1.000000e-04 +2114 1968 1963 -4.104744e-01 -3.364586e-01 8.475296e-01 -1.000000e-04 +1969 2118 1964 -2.729509e-01 -4.430233e-01 -8.539486e-01 -1.000000e-04 +2120 1967 2119 -8.338581e-01 -3.773898e-01 4.028120e-01 -1.000000e-04 +1966 1970 2117 1.268180e-01 -4.297221e-01 -8.940113e-01 -1.000000e-04 +2118 1969 2121 -1.678801e-01 -5.037899e-01 -8.473559e-01 -1.000000e-04 +2122 2117 1970 6.145265e-02 -3.982008e-01 -9.152375e-01 -1.000000e-04 +1968 2114 2123 -7.410940e-01 -3.123660e-01 5.943124e-01 -1.000000e-04 +1971 2120 2124 -7.628278e-01 -2.264760e-01 6.056422e-01 -1.000000e-04 +2120 1971 1967 -7.431113e-01 -2.393293e-01 6.249057e-01 -1.000000e-04 +1972 1968 2123 -7.761832e-01 -4.673248e-01 4.232578e-01 -1.000000e-04 +1973 2121 1969 -2.056044e-02 -3.866742e-01 -9.219872e-01 -1.000000e-04 +2124 1974 1971 -6.684866e-01 -1.716259e-01 7.236506e-01 -1.000000e-04 +1970 2125 2122 1.168636e-01 -3.822466e-01 -9.166408e-01 -1.000000e-04 +2125 1970 1975 2.041757e-01 -2.819279e-01 -9.374588e-01 -1.000000e-04 +2123 2126 1972 -7.772892e-01 -4.666266e-01 4.219966e-01 -1.000000e-04 +2121 1973 2127 -6.037561e-04 -3.975220e-01 -9.175925e-01 -1.000000e-04 +1974 2124 2128 -6.983493e-01 -1.573326e-01 6.982512e-01 -1.000000e-04 +1976 1972 2126 -7.738454e-01 -5.767973e-01 2.616641e-01 -1.000000e-04 +2127 1973 2129 1.503656e-01 -3.698944e-01 -9.168251e-01 -1.000000e-04 +2128 1977 1974 -6.028726e-01 -1.086530e-01 7.904044e-01 -1.000000e-04 +1977 2128 2130 -6.429124e-01 -8.372543e-02 7.613499e-01 -1.000000e-04 +1975 2131 2125 1.026081e-01 -2.703728e-01 -9.572722e-01 -1.000000e-04 +2131 1975 1978 1.199884e-01 -2.555651e-01 -9.593171e-01 -1.000000e-04 +1979 2129 1973 2.730568e-01 -2.806278e-01 -9.201565e-01 -1.000000e-04 +2126 2132 1976 -6.399888e-01 -6.717486e-01 3.730525e-01 -1.000000e-04 +2129 1979 2133 2.170858e-01 -2.498996e-01 -9.436228e-01 -1.000000e-04 +2132 1980 1976 -6.362835e-01 -6.663856e-01 3.886819e-01 -1.000000e-04 +2130 1981 1977 -5.142186e-01 3.700346e-02 8.568605e-01 -1.000000e-04 +1978 2134 2131 3.101118e-02 -2.117036e-01 -9.768418e-01 -1.000000e-04 +1980 2132 2135 -5.499130e-01 -6.955997e-01 4.623167e-01 -1.000000e-04 +1982 2133 1979 1.907813e-01 -2.618926e-01 -9.460522e-01 -1.000000e-04 +2133 1982 2136 2.317729e-01 -2.834158e-01 -9.305680e-01 -1.000000e-04 +2134 1978 2137 3.707458e-02 -2.089231e-01 -9.772290e-01 -1.000000e-04 +2135 2138 1980 -5.024646e-01 -6.176780e-01 6.049820e-01 -1.000000e-04 +1980 2138 1983 -4.773565e-01 -6.774473e-01 5.596391e-01 -1.000000e-04 +2130 2139 1981 -5.001340e-01 3.467599e-02 8.652535e-01 -1.000000e-04 +1981 2139 1984 -4.121653e-01 1.306990e-01 9.016860e-01 -1.000000e-04 +1984 2139 2140 -4.179257e-01 1.318575e-01 8.988614e-01 -1.000000e-04 +1986 2137 1978 1.047297e-01 -1.264833e-01 -9.864247e-01 -1.000000e-04 +2137 1986 2141 1.099611e-01 -1.283566e-01 -9.856131e-01 -1.000000e-04 +2138 1987 1983 -4.052558e-01 -4.455945e-01 7.982564e-01 -1.000000e-04 +2142 2138 2135 -5.899890e-01 -5.588866e-01 5.827167e-01 -1.000000e-04 +1985 2136 1982 1.745299e-01 -3.091120e-01 -9.348738e-01 -1.000000e-04 +2136 1985 2143 3.584380e-01 -3.641527e-01 -8.596017e-01 -1.000000e-04 +1988 2141 1986 1.382293e-01 -1.023128e-01 -9.851014e-01 -1.000000e-04 +2142 1987 2138 -4.912691e-01 -3.273938e-01 8.071356e-01 -1.000000e-04 +2140 1989 1984 -2.735966e-01 2.451981e-01 9.300660e-01 -1.000000e-04 +1991 2143 1985 2.022182e-01 -4.288855e-01 -8.804346e-01 -1.000000e-04 +2143 1991 2144 4.405832e-01 -4.964154e-01 -7.479694e-01 -1.000000e-04 +2145 1987 2142 -6.286519e-01 -2.810007e-01 7.251451e-01 -1.000000e-04 +2144 1991 1992 1.311196e-01 -7.127284e-01 -6.890761e-01 -1.000000e-04 +2146 1989 2140 -1.745356e-01 2.036983e-01 9.633506e-01 -1.000000e-04 +1993 2141 1988 1.887634e-01 -8.521026e-02 -9.783188e-01 -1.000000e-04 +1989 2146 2147 -1.019980e-01 2.323206e-01 9.672763e-01 -1.000000e-04 +2148 2141 1993 1.402021e-01 -4.768412e-02 -9.889740e-01 -1.000000e-04 +2145 1994 1987 -4.019746e-01 8.621066e-02 9.115833e-01 -1.000000e-04 +2147 1995 1989 -2.223193e-01 1.326093e-01 9.659135e-01 -1.000000e-04 +1995 2147 2149 -1.507212e-01 9.057454e-02 9.844183e-01 -1.000000e-04 +2148 1993 1996 1.634653e-01 -3.447345e-02 -9.859466e-01 -1.000000e-04 +2145 1997 1994 -2.566997e-01 4.423605e-02 9.654783e-01 -1.000000e-04 +1997 2145 2150 -5.156330e-01 2.880911e-01 8.069239e-01 -1.000000e-04 +1992 2151 2144 1.976471e-01 -7.089113e-01 -6.770379e-01 -1.000000e-04 +2148 1996 2152 1.393898e-01 -2.801828e-02 -9.898411e-01 -1.000000e-04 +2151 1992 2153 1.896198e-01 -7.135983e-01 -6.744048e-01 -1.000000e-04 +2153 1992 1999 9.269960e-02 -8.162738e-01 -5.701788e-01 -1.000000e-04 +2000 2152 1996 6.728959e-02 -9.274300e-02 -9.934137e-01 -1.000000e-04 +2152 2000 2154 7.240096e-02 -9.532859e-02 -9.928094e-01 -1.000000e-04 +1997 2150 2001 -2.218766e-01 4.105506e-01 8.844315e-01 -1.000000e-04 +2155 2151 2153 9.197462e-02 -7.089948e-01 -6.991903e-01 -1.000000e-04 +1999 2155 2153 -1.074221e-02 -8.077206e-01 -5.894675e-01 -1.000000e-04 +2001 2150 2156 -3.649831e-01 5.127483e-01 7.770949e-01 -1.000000e-04 +1999 2002 2155 7.911967e-02 -7.735453e-01 -6.287827e-01 -1.000000e-04 +2149 2003 1995 -6.302914e-01 -1.516051e-01 7.614123e-01 -1.000000e-04 +2003 2149 2157 -5.296963e-01 -2.268774e-01 8.172812e-01 -1.000000e-04 +2001 2156 2158 -3.715143e-01 5.129471e-01 7.738620e-01 -1.000000e-04 +2003 2157 2159 -7.538255e-01 -2.263598e-01 6.168535e-01 -1.000000e-04 +2004 2001 2158 -3.430360e-01 5.403856e-01 7.683161e-01 -1.000000e-04 +2002 2160 2155 -8.941164e-02 -7.414938e-01 -6.649755e-01 -1.000000e-04 +2003 2159 2006 -8.134699e-01 -3.316358e-01 4.777912e-01 -1.000000e-04 +2000 2007 2154 -2.505455e-01 -2.964168e-01 -9.216095e-01 -1.000000e-04 +2160 2002 2005 1.650700e-02 -7.233583e-01 -6.902755e-01 -1.000000e-04 +2007 2161 2154 -2.913226e-01 -2.731599e-01 -9.167960e-01 -1.000000e-04 +2162 2160 2005 -2.792402e-01 -6.597297e-01 -6.976974e-01 -1.000000e-04 +2162 2005 2008 -2.313453e-01 -6.329455e-01 -7.388230e-01 -1.000000e-04 +2163 2009 2006 -9.035573e-01 -3.380128e-01 2.633089e-01 -1.000000e-04 +2163 2006 2159 -8.776574e-01 -2.851535e-01 3.852336e-01 -1.000000e-04 +2007 2164 2161 -3.795994e-01 -3.168243e-01 -8.692103e-01 -1.000000e-04 +2007 2010 2164 -4.085309e-01 -3.729929e-01 -8.330539e-01 -1.000000e-04 +2004 2158 2165 -4.721973e-01 5.394242e-01 6.971737e-01 -1.000000e-04 +2009 2166 2011 -9.105234e-01 -3.893360e-01 1.391565e-01 -1.000000e-04 +2009 2163 2166 -9.106353e-01 -3.319705e-01 2.460468e-01 -1.000000e-04 +2010 2167 2164 -3.934399e-01 -3.718693e-01 -8.407843e-01 -1.000000e-04 +2010 2012 2167 -3.795095e-01 -3.466405e-01 -8.577954e-01 -1.000000e-04 +2165 2013 2004 -6.547540e-01 3.995660e-01 6.415951e-01 -1.000000e-04 +2013 2165 2168 -6.265881e-01 3.890184e-01 6.753162e-01 -1.000000e-04 +2162 2008 2169 -5.671213e-01 -4.938506e-01 -6.591547e-01 -1.000000e-04 +2014 2169 2008 -6.026617e-01 -5.136645e-01 -6.106945e-01 -1.000000e-04 +2011 2166 2170 -9.101916e-01 -3.898532e-01 1.398774e-01 -1.000000e-04 +2167 2012 2015 -4.255579e-01 -3.654217e-01 -8.278693e-01 -1.000000e-04 +2169 2014 2171 -7.381692e-01 -4.090180e-01 -5.364797e-01 -1.000000e-04 +2016 2171 2014 -7.165436e-01 -3.898513e-01 -5.784300e-01 -1.000000e-04 +2170 2018 2011 -9.104545e-01 -3.902425e-01 1.370522e-01 -1.000000e-04 +2018 2170 2172 -9.406717e-01 -3.336346e-01 6.184422e-02 -1.000000e-04 +2013 2168 2173 -7.924336e-01 3.099062e-01 5.253639e-01 -1.000000e-04 +2013 2173 2019 -8.866326e-01 1.331362e-01 4.428965e-01 -1.000000e-04 +2171 2016 2174 -7.229029e-01 -3.856770e-01 -5.732928e-01 -1.000000e-04 +2017 2174 2016 -7.084217e-01 -3.591154e-01 -6.075975e-01 -1.000000e-04 +2020 2175 2017 -7.970674e-01 -3.623361e-01 -4.831108e-01 -1.000000e-04 +2017 2175 2174 -7.903681e-01 -3.477635e-01 -5.043599e-01 -1.000000e-04 +2022 2176 2021 -9.462424e-01 -2.720495e-01 -1.749696e-01 -1.000000e-04 +2176 2022 2172 -9.468931e-01 -2.707045e-01 -1.735294e-01 -1.000000e-04 +2018 2172 2022 -9.402280e-01 -3.384974e-01 3.729479e-02 -1.000000e-04 +2167 2015 2177 -4.895326e-01 -3.379371e-01 -8.038385e-01 -1.000000e-04 +2177 2015 2178 -5.507219e-01 -3.736497e-01 -7.463855e-01 -1.000000e-04 +2015 2023 2178 -5.482246e-01 -3.680770e-01 -7.509788e-01 -1.000000e-04 +2175 2020 2179 -8.801573e-01 -2.848869e-01 -3.796876e-01 -1.000000e-04 +2021 2179 2020 -9.031218e-01 -2.860344e-01 -3.202425e-01 -1.000000e-04 +2179 2021 2176 -9.175534e-01 -2.605511e-01 -3.003479e-01 -1.000000e-04 +2023 2024 2178 -6.182839e-01 -3.688277e-01 -6.940398e-01 -1.000000e-04 +2180 2025 2173 -9.621184e-01 3.593664e-02 2.702532e-01 -1.000000e-04 +2173 2025 2019 -9.705128e-01 8.010037e-02 2.273518e-01 -1.000000e-04 +2178 2024 2181 -6.321889e-01 -3.580288e-01 -6.871335e-01 -1.000000e-04 +2024 2026 2181 -6.424270e-01 -3.696765e-01 -6.712875e-01 -1.000000e-04 +2181 2026 2182 -7.337485e-01 -2.966896e-01 -6.112188e-01 -1.000000e-04 +2029 2183 2184 -9.639682e-01 -2.356774e-01 -1.233753e-01 -1.000000e-04 +2030 2183 2029 -9.641302e-01 -2.356731e-01 -1.221113e-01 -1.000000e-04 +2183 2030 2180 -9.892050e-01 -1.433934e-01 -3.019750e-02 -1.000000e-04 +2180 2030 2025 -9.897242e-01 -1.379192e-01 -3.774041e-02 -1.000000e-04 +2182 2026 2185 -7.779109e-01 -3.045739e-01 -5.496266e-01 -1.000000e-04 +2027 2185 2026 -7.637876e-01 -2.834726e-01 -5.798895e-01 -1.000000e-04 +2185 2027 2186 -8.615162e-01 -2.161019e-01 -4.594452e-01 -1.000000e-04 +2031 2186 2027 -8.735589e-01 -2.277315e-01 -4.301549e-01 -1.000000e-04 +2186 2031 2187 -9.141577e-01 -1.787950e-01 -3.637967e-01 -1.000000e-04 +2028 2187 2031 -9.239512e-01 -2.091380e-01 -3.202741e-01 -1.000000e-04 +2187 2028 2184 -9.497437e-01 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