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from sympy.physics.mechanics import Point, ReferenceFrame, Dyadic, RigidBody
from sympy.physics.mechanics import dynamicsymbols, outer, inertia, Inertia
from sympy.physics.mechanics import inertia_of_point_mass
from sympy import expand, zeros, simplify, symbols
from sympy.testing.pytest import raises, warns_deprecated_sympy
def test_rigidbody_default():
# Test default
b = RigidBody('B')
I = inertia(b.frame, *symbols('B_ixx B_iyy B_izz B_ixy B_iyz B_izx'))
assert b.name == 'B'
assert b.mass == symbols('B_mass')
assert b.masscenter.name == 'B_masscenter'
assert b.inertia == (I, b.masscenter)
assert b.central_inertia == I
assert b.frame.name == 'B_frame'
assert b.__str__() == 'B'
assert b.__repr__() == (
"RigidBody('B', masscenter=B_masscenter, frame=B_frame, mass=B_mass, "
"inertia=Inertia(dyadic=B_ixx*(B_frame.x|B_frame.x) + "
"B_ixy*(B_frame.x|B_frame.y) + B_izx*(B_frame.x|B_frame.z) + "
"B_ixy*(B_frame.y|B_frame.x) + B_iyy*(B_frame.y|B_frame.y) + "
"B_iyz*(B_frame.y|B_frame.z) + B_izx*(B_frame.z|B_frame.x) + "
"B_iyz*(B_frame.z|B_frame.y) + B_izz*(B_frame.z|B_frame.z), "
"point=B_masscenter))")
def test_rigidbody():
m, m2, v1, v2, v3, omega = symbols('m m2 v1 v2 v3 omega')
A = ReferenceFrame('A')
A2 = ReferenceFrame('A2')
P = Point('P')
P2 = Point('P2')
I = Dyadic(0)
I2 = Dyadic(0)
B = RigidBody('B', P, A, m, (I, P))
assert B.mass == m
assert B.frame == A
assert B.masscenter == P
assert B.inertia == (I, B.masscenter)
B.mass = m2
B.frame = A2
B.masscenter = P2
B.inertia = (I2, B.masscenter)
raises(TypeError, lambda: RigidBody(P, P, A, m, (I, P)))
raises(TypeError, lambda: RigidBody('B', P, P, m, (I, P)))
raises(TypeError, lambda: RigidBody('B', P, A, m, (P, P)))
raises(TypeError, lambda: RigidBody('B', P, A, m, (I, I)))
assert B.__str__() == 'B'
assert B.mass == m2
assert B.frame == A2
assert B.masscenter == P2
assert B.inertia == (I2, B.masscenter)
assert isinstance(B.inertia, Inertia)
# Testing linear momentum function assuming A2 is the inertial frame
N = ReferenceFrame('N')
P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
assert B.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)
def test_rigidbody2():
M, v, r, omega, g, h = dynamicsymbols('M v r omega g h')
N = ReferenceFrame('N')
b = ReferenceFrame('b')
b.set_ang_vel(N, omega * b.x)
P = Point('P')
I = outer(b.x, b.x)
Inertia_tuple = (I, P)
B = RigidBody('B', P, b, M, Inertia_tuple)
P.set_vel(N, v * b.x)
assert B.angular_momentum(P, N) == omega * b.x
O = Point('O')
O.set_vel(N, v * b.x)
P.set_pos(O, r * b.y)
assert B.angular_momentum(O, N) == omega * b.x - M*v*r*b.z
B.potential_energy = M * g * h
assert B.potential_energy == M * g * h
assert expand(2 * B.kinetic_energy(N)) == omega**2 + M * v**2
def test_rigidbody3():
q1, q2, q3, q4 = dynamicsymbols('q1:5')
p1, p2, p3 = symbols('p1:4')
m = symbols('m')
A = ReferenceFrame('A')
B = A.orientnew('B', 'axis', [q1, A.x])
O = Point('O')
O.set_vel(A, q2*A.x + q3*A.y + q4*A.z)
P = O.locatenew('P', p1*B.x + p2*B.y + p3*B.z)
P.v2pt_theory(O, A, B)
I = outer(B.x, B.x)
rb1 = RigidBody('rb1', P, B, m, (I, P))
# I_S/O = I_S/S* + I_S*/O
rb2 = RigidBody('rb2', P, B, m,
(I + inertia_of_point_mass(m, P.pos_from(O), B), O))
assert rb1.central_inertia == rb2.central_inertia
assert rb1.angular_momentum(O, A) == rb2.angular_momentum(O, A)
def test_pendulum_angular_momentum():
"""Consider a pendulum of length OA = 2a, of mass m as a rigid body of
center of mass G (OG = a) which turn around (O,z). The angle between the
reference frame R and the rod is q. The inertia of the body is I =
(G,0,ma^2/3,ma^2/3). """
m, a = symbols('m, a')
q = dynamicsymbols('q')
R = ReferenceFrame('R')
R1 = R.orientnew('R1', 'Axis', [q, R.z])
R1.set_ang_vel(R, q.diff() * R.z)
I = inertia(R1, 0, m * a**2 / 3, m * a**2 / 3)
O = Point('O')
A = O.locatenew('A', 2*a * R1.x)
G = O.locatenew('G', a * R1.x)
S = RigidBody('S', G, R1, m, (I, G))
O.set_vel(R, 0)
A.v2pt_theory(O, R, R1)
G.v2pt_theory(O, R, R1)
assert (4 * m * a**2 / 3 * q.diff() * R.z -
S.angular_momentum(O, R).express(R)) == 0
def test_rigidbody_inertia():
N = ReferenceFrame('N')
m, Ix, Iy, Iz, a, b = symbols('m, I_x, I_y, I_z, a, b')
Io = inertia(N, Ix, Iy, Iz)
o = Point('o')
p = o.locatenew('p', a * N.x + b * N.y)
R = RigidBody('R', o, N, m, (Io, p))
I_check = inertia(N, Ix - b ** 2 * m, Iy - a ** 2 * m,
Iz - m * (a ** 2 + b ** 2), m * a * b)
assert isinstance(R.inertia, Inertia)
assert R.inertia == (Io, p)
assert R.central_inertia == I_check
R.central_inertia = Io
assert R.inertia == (Io, o)
assert R.central_inertia == Io
R.inertia = (Io, p)
assert R.inertia == (Io, p)
assert R.central_inertia == I_check
# parse Inertia object
R.inertia = Inertia(Io, o)
assert R.inertia == (Io, o)
def test_parallel_axis():
N = ReferenceFrame('N')
m, Ix, Iy, Iz, a, b = symbols('m, I_x, I_y, I_z, a, b')
Io = inertia(N, Ix, Iy, Iz)
o = Point('o')
p = o.locatenew('p', a * N.x + b * N.y)
R = RigidBody('R', o, N, m, (Io, o))
Ip = R.parallel_axis(p)
Ip_expected = inertia(N, Ix + m * b**2, Iy + m * a**2,
Iz + m * (a**2 + b**2), ixy=-m * a * b)
assert Ip == Ip_expected
# Reference frame from which the parallel axis is viewed should not matter
A = ReferenceFrame('A')
A.orient_axis(N, N.z, 1)
assert simplify(
(R.parallel_axis(p, A) - Ip_expected).to_matrix(A)) == zeros(3, 3)
def test_deprecated_set_potential_energy():
m, g, h = symbols('m g h')
A = ReferenceFrame('A')
P = Point('P')
I = Dyadic(0)
B = RigidBody('B', P, A, m, (I, P))
with warns_deprecated_sympy():
B.set_potential_energy(m*g*h)
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