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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) | |