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test_point.py
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test_point.py
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from sympy.physics.vector import dynamicsymbols, Point, ReferenceFrame
from sympy.testing.pytest import raises, ignore_warnings
import warnings
def test_point_v1pt_theorys():
q, q2 = dynamicsymbols('q q2')
qd, q2d = dynamicsymbols('q q2', 1)
qdd, q2dd = dynamicsymbols('q q2', 2)
N = ReferenceFrame('N')
B = ReferenceFrame('B')
B.set_ang_vel(N, qd * B.z)
O = Point('O')
P = O.locatenew('P', B.x)
P.set_vel(B, 0)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.y
O.set_vel(N, N.x)
assert P.v1pt_theory(O, N, B) == N.x + qd * B.y
P.set_vel(B, B.z)
assert P.v1pt_theory(O, N, B) == B.z + N.x + qd * B.y
def test_point_a1pt_theorys():
q, q2 = dynamicsymbols('q q2')
qd, q2d = dynamicsymbols('q q2', 1)
qdd, q2dd = dynamicsymbols('q q2', 2)
N = ReferenceFrame('N')
B = ReferenceFrame('B')
B.set_ang_vel(N, qd * B.z)
O = Point('O')
P = O.locatenew('P', B.x)
P.set_vel(B, 0)
O.set_vel(N, 0)
assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y
P.set_vel(B, q2d * B.z)
assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y + q2dd * B.z
O.set_vel(N, q2d * B.x)
assert P.a1pt_theory(O, N, B) == ((q2dd - qd**2) * B.x + (q2d * qd + qdd) * B.y +
q2dd * B.z)
def test_point_v2pt_theorys():
q = dynamicsymbols('q')
qd = dynamicsymbols('q', 1)
N = ReferenceFrame('N')
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 0)
O.set_vel(N, 0)
assert P.v2pt_theory(O, N, B) == 0
P = O.locatenew('P', B.x)
assert P.v2pt_theory(O, N, B) == (qd * B.z ^ B.x)
O.set_vel(N, N.x)
assert P.v2pt_theory(O, N, B) == N.x + qd * B.y
def test_point_a2pt_theorys():
q = dynamicsymbols('q')
qd = dynamicsymbols('q', 1)
qdd = dynamicsymbols('q', 2)
N = ReferenceFrame('N')
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 0)
O.set_vel(N, 0)
assert P.a2pt_theory(O, N, B) == 0
P.set_pos(O, B.x)
assert P.a2pt_theory(O, N, B) == (-qd**2) * B.x + (qdd) * B.y
def test_point_funcs():
q, q2 = dynamicsymbols('q q2')
qd, q2d = dynamicsymbols('q q2', 1)
qdd, q2dd = dynamicsymbols('q q2', 2)
N = ReferenceFrame('N')
B = ReferenceFrame('B')
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
assert P.pos_from(O) == q * B.x
P.set_vel(B, qd * B.x + q2d * B.y)
assert P.vel(B) == qd * B.x + q2d * B.y
O.set_vel(N, 0)
assert O.vel(N) == 0
assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
(-10 * qd) * B.z)
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 10 * B.x)
O.set_vel(N, 5 * N.x)
assert O.vel(N) == 5 * N.x
assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
P.set_vel(B, qd * B.x + q2d * B.y)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
def test_point_pos():
q = dynamicsymbols('q')
N = ReferenceFrame('N')
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 10 * N.x + 5 * B.x)
assert P.pos_from(O) == 10 * N.x + 5 * B.x
Q = P.locatenew('Q', 10 * N.y + 5 * B.y)
assert Q.pos_from(P) == 10 * N.y + 5 * B.y
assert Q.pos_from(O) == 10 * N.x + 10 * N.y + 5 * B.x + 5 * B.y
assert O.pos_from(Q) == -10 * N.x - 10 * N.y - 5 * B.x - 5 * B.y
def test_point_partial_velocity():
N = ReferenceFrame('N')
A = ReferenceFrame('A')
p = Point('p')
u1, u2 = dynamicsymbols('u1, u2')
p.set_vel(N, u1 * A.x + u2 * N.y)
assert p.partial_velocity(N, u1) == A.x
assert p.partial_velocity(N, u1, u2) == (A.x, N.y)
raises(ValueError, lambda: p.partial_velocity(A, u1))
def test_point_vel(): #Basic functionality
q1, q2 = dynamicsymbols('q1 q2')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
Q = Point('Q')
O = Point('O')
Q.set_pos(O, q1 * N.x)
raises(ValueError , lambda: Q.vel(N)) # Velocity of O in N is not defined
O.set_vel(N, q2 * N.y)
assert O.vel(N) == q2 * N.y
raises(ValueError , lambda : O.vel(B)) #Velocity of O is not defined in B
def test_auto_point_vel():
t = dynamicsymbols._t
q1, q2 = dynamicsymbols('q1 q2')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
O = Point('O')
Q = Point('Q')
Q.set_pos(O, q1 * N.x)
O.set_vel(N, q2 * N.y)
assert Q.vel(N) == q1.diff(t) * N.x + q2 * N.y # Velocity of Q using O
P1 = Point('P1')
P1.set_pos(O, q1 * B.x)
P2 = Point('P2')
P2.set_pos(P1, q2 * B.z)
raises(ValueError, lambda : P2.vel(B)) # O's velocity is defined in different frame, and no
#point in between has its velocity defined
raises(ValueError, lambda: P2.vel(N)) # Velocity of O not defined in N
def test_auto_point_vel_multiple_point_path():
t = dynamicsymbols._t
q1, q2 = dynamicsymbols('q1 q2')
B = ReferenceFrame('B')
P = Point('P')
P.set_vel(B, q1 * B.x)
P1 = Point('P1')
P1.set_pos(P, q2 * B.y)
P1.set_vel(B, q1 * B.z)
P2 = Point('P2')
P2.set_pos(P1, q1 * B.z)
P3 = Point('P3')
P3.set_pos(P2, 10 * q1 * B.y)
assert P3.vel(B) == 10 * q1.diff(t) * B.y + (q1 + q1.diff(t)) * B.z
def test_auto_vel_dont_overwrite():
t = dynamicsymbols._t
q1, q2, u1 = dynamicsymbols('q1, q2, u1')
N = ReferenceFrame('N')
P = Point('P1')
P.set_vel(N, u1 * N.x)
P1 = Point('P1')
P1.set_pos(P, q2 * N.y)
assert P1.vel(N) == q2.diff(t) * N.y + u1 * N.x
assert P.vel(N) == u1 * N.x
P1.set_vel(N, u1 * N.z)
assert P1.vel(N) == u1 * N.z
def test_auto_point_vel_if_tree_has_vel_but_inappropriate_pos_vector():
q1, q2 = dynamicsymbols('q1 q2')
B = ReferenceFrame('B')
S = ReferenceFrame('S')
P = Point('P')
P.set_vel(B, q1 * B.x)
P1 = Point('P1')
P1.set_pos(P, S.y)
raises(ValueError, lambda : P1.vel(B)) # P1.pos_from(P) can't be expressed in B
raises(ValueError, lambda : P1.vel(S)) # P.vel(S) not defined
def test_auto_point_vel_shortest_path():
t = dynamicsymbols._t
q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
B = ReferenceFrame('B')
P = Point('P')
P.set_vel(B, u1 * B.x)
P1 = Point('P1')
P1.set_pos(P, q2 * B.y)
P1.set_vel(B, q1 * B.z)
P2 = Point('P2')
P2.set_pos(P1, q1 * B.z)
P3 = Point('P3')
P3.set_pos(P2, 10 * q1 * B.y)
P4 = Point('P4')
P4.set_pos(P3, q1 * B.x)
O = Point('O')
O.set_vel(B, u2 * B.y)
O1 = Point('O1')
O1.set_pos(O, q2 * B.z)
P4.set_pos(O1, q1 * B.x + q2 * B.z)
with warnings.catch_warnings():
warnings.simplefilter('error')
with ignore_warnings(UserWarning):
assert P4.vel(B) == q1.diff(t) * B.x + u2 * B.y + 2 * q2.diff(t) * B.z
def test_auto_point_vel_connected_frames():
t = dynamicsymbols._t
q, q1, q2, u = dynamicsymbols('q q1 q2 u')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
O = Point('O')
O.set_vel(N, u * N.x)
P = Point('P')
P.set_pos(O, q1 * N.x + q2 * B.y)
raises(ValueError, lambda: P.vel(N))
N.orient(B, 'Axis', (q, B.x))
assert P.vel(N) == (u + q1.diff(t)) * N.x + q2.diff(t) * B.y - q2 * q.diff(t) * B.z
def test_auto_point_vel_multiple_paths_warning_arises():
q, u = dynamicsymbols('q u')
N = ReferenceFrame('N')
O = Point('O')
P = Point('P')
Q = Point('Q')
R = Point('R')
P.set_vel(N, u * N.x)
Q.set_vel(N, u *N.y)
R.set_vel(N, u * N.z)
O.set_pos(P, q * N.z)
O.set_pos(Q, q * N.y)
O.set_pos(R, q * N.x)
with warnings.catch_warnings():
warnings.simplefilter("error")
raises(UserWarning ,lambda: O.vel(N))
def test_auto_vel_cyclic_warning_arises():
P = Point('P')
P1 = Point('P1')
P2 = Point('P2')
P3 = Point('P3')
N = ReferenceFrame('N')
P.set_vel(N, N.x)
P1.set_pos(P, N.x)
P2.set_pos(P1, N.y)
P3.set_pos(P2, N.z)
P1.set_pos(P3, N.x + N.y)
with warnings.catch_warnings():
warnings.simplefilter("error")
raises(UserWarning ,lambda: P2.vel(N))
def test_auto_vel_cyclic_warning_msg():
P = Point('P')
P1 = Point('P1')
P2 = Point('P2')
P3 = Point('P3')
N = ReferenceFrame('N')
P.set_vel(N, N.x)
P1.set_pos(P, N.x)
P2.set_pos(P1, N.y)
P3.set_pos(P2, N.z)
P1.set_pos(P3, N.x + N.y)
with warnings.catch_warnings(record = True) as w:
warnings.simplefilter("always")
P2.vel(N)
assert issubclass(w[-1].category, UserWarning)
assert 'Multiple points have their position defined with respect to one point.' in str(w[-1].message)
def test_auto_vel_multiple_path_warning_msg():
N = ReferenceFrame('N')
O = Point('O')
P = Point('P')
Q = Point('Q')
P.set_vel(N, N.x)
Q.set_vel(N, N.y)
O.set_pos(P, N.z)
O.set_pos(Q, N.y)
with warnings.catch_warnings(record = True) as w:
warnings.simplefilter("always")
O.vel(N)
assert issubclass(w[-1].category, UserWarning)
assert 'Velocity automatically calculated based on point' in str(w[-1].message)
assert 'Velocities from these points are not the same.' in str(w[-1].message)