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