ObjectMassPoint.rst

ObjectMassPoint

A 3D mass point which is attached to a position-based node, usually NodePoint.

Additional information for ObjectMassPoint:

• This Object has/provides the following types = Body, SingleNoded
• Requested Node type = Position
• Short name for Python = MassPoint
• Short name for Python visualization object = VMassPoint

The item ObjectMassPoint with type = 'MassPoint' has the following parameters:

• name [type = String, default = '']:

  objects's unique name
• physicsMass [m, type = UReal, default = 0.]:

  mass [SI:kg] of mass point
• nodeNumber [n0, type = NodeIndex, default = invalid (-1)]:

  node number (type NodeIndex) for mass point
• visualization [type = VObjectMassPoint]:

  parameters for visualization of item

The item VObjectMassPoint has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown
• graphicsData [type = BodyGraphicsData]:

  Structure contains data for body visualization; data is defined in special list / dictionary structure

---

DESCRIPTION of ObjectMassPoint

The following output variables are available as OutputVariableType in sensors, Get...Output() and other functions:

• Position: \LU{0}{{\mathbf{p}}}\cConfig(\pLocB) = \LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef + \LU{0b}{\mathbf{I}_{3 \times 3}}\pLocB

  global position vector of translated local position; local (body) coordinate system = global coordinate system
• Displacement: \LU{0}{{\mathbf{u}}}\cConfig = [q_0,\;q_1,\;q_2]\cConfig\tp

  global displacement vector of mass point
• Velocity: \LU{0}{{\mathbf{v}}}\cConfig = \LU{0}{\dot{\mathbf{u}}}\cConfig = [\dot q_0,\;\dot q_1,\;\dot q_2]\cConfig\tp

  global velocity vector of mass point
• Acceleration: \LU{0}{{\mathbf{a}}}\cConfig = \LU{0}{\ddot{\mathbf{u}}}\cConfig = [\ddot q_0,\;\ddot q_1,\;\ddot q_2]\cConfig\tp

  global acceleration vector of mass point

Definition of quantities

intermediate variables	symbol	description
node position	\LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef = \LU{0}{{\mathbf{p}}}(n_0)\cConfig	position of mass point which is provided by node n_0 in any configuration
node displacement	\LU{0}{{\mathbf{u}}}\cConfig = \LU{0}{\pRef}\cConfig = [q_0,\;q_1,\;q_2]\cConfig\tp = \LU{0}{{\mathbf{u}}}(n_0)\cConfig	displacement of mass point which is provided by node n_0 in any configuration
node velocity	\LU{0}{{\mathbf{v}}}\cConfig = [\dot q_0,\;\dot q_1,\;\dot q_2]\cConfig\tp = \LU{0}{{\mathbf{v}}}(n_0)\cConfig	velocity of mass point which is provided by node n_0 in any configuration
transformation matrix	\LU{0b}{\Rot} = \mathbf{I}_{3 \times 3}	transformation of local body (b) coordinates to global (0) coordinates; this is the constant unit matrix, because local = global coordinates for the mass point
residual forces	\LU{0}{{\mathbf{f}}} = [f_0,\;f_1,\;f_2]\tp	residual of all forces on mass point
applied forces	\LU{0}{{\mathbf{f}}}_a = [f_0,\;f_1,\;f_2]\tp	applied forces (loads, connectors, joint reaction forces, ...)

Equations of motion

\mr{m}{0}{0} {0}{m}{0} {0}{0}{m} \vr{\ddot q_0}{\ddot q_1}{\ddot q_2} = \vr{f_0}{f_1}{f_2}.

For example, a LoadCoordinate on coordinate 1 of the node would add a term in f_1 on the RHS.

Position-based markers can measure position {\mathbf{p}}\cConfig. The position jacobian

{\mathbf{J}}_{pos} = \partial {\mathbf{p}}\cCur / \partial {\mathbf{c}}\cCur = \mr{1}{0}{0} {0}{1}{0} {0}{0}{0}

transforms the action of global applied forces \LU{0}{{\mathbf{f}}}_a of position-based markers on the coordinates {\mathbf{c}}

{\mathbf{Q}} = {\mathbf{J}}_{pos} \LU{0}{{\mathbf{f}}}_a.

MINI EXAMPLE for ObjectMassPoint

node = mbs.AddNode(NodePoint(referenceCoordinates = [1,1,0],
                             initialCoordinates=[0.5,0,0],
                             initialVelocities=[0.5,0,0]))
mbs.AddObject(MassPoint(nodeNumber = node, physicsMass=1))

#assemble and solve system for default parameters
mbs.Assemble()
mbs.SolveDynamic()

#check result
exudynTestGlobals.testResult = mbs.GetNodeOutput(node, exu.OutputVariableType.Position)[0]
#final x-coordinate of position shall be 2

Relevant Examples and TestModels with weblink:

interactiveTutorial.py (Examples/), ComputeSensitivitiesExample.py (Examples/), coordinateSpringDamper.py (Examples/), massSpringFrictionInteractive.py (Examples/), minimizeExample.py (Examples/), nMassOscillator.py (Examples/), nMassOscillatorInteractive.py (Examples/), parameterVariationExample.py (Examples/), particleClusters.py (Examples/), particlesSilo.py (Examples/), particlesTest.py (Examples/), particlesTest3D.py (Examples/), complexEigenvaluesTest.py (TestModels/), connectorGravityTest.py (TestModels/), contactCoordinateTest.py (TestModels/)

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf