def test_pinjoint(): P = Body('P') C = Body('C') l, m = symbols('l m') theta, omega = dynamicsymbols('theta_J, omega_J') Pj = PinJoint('J', P, C) assert Pj.name == 'J' assert Pj.parent == P assert Pj.child == C assert Pj.coordinates == [theta] assert Pj.speeds == [omega] assert Pj.kdes == [omega - theta.diff(t)] assert Pj.parent_axis == P.frame.x assert Pj.child_point.pos_from(C.masscenter) == Vector(0) assert Pj.parent_point.pos_from(P.masscenter) == Vector(0) assert Pj.parent_point.pos_from(Pj._child_point) == Vector(0) assert C.masscenter.pos_from(P.masscenter) == Vector(0) assert Pj.__str__() == 'PinJoint: J parent: P child: C' P1 = Body('P1') C1 = Body('C1') J1 = PinJoint('J1', P1, C1, parent_joint_pos=l*P1.frame.x, child_joint_pos=m*C1.frame.y, parent_axis=P1.frame.z) assert J1._parent_axis == P1.frame.z assert J1._child_point.pos_from(C1.masscenter) == m * C1.frame.y assert J1._parent_point.pos_from(P1.masscenter) == l * P1.frame.x assert J1._parent_point.pos_from(J1._child_point) == Vector(0) assert (P1.masscenter.pos_from(C1.masscenter) == -l*P1.frame.x + m*C1.frame.y)
def test_body_masscenter_vel(): A = Body('A') N = ReferenceFrame('N') B = Body('B', frame=N) A.masscenter.set_vel(N, N.z) assert A.masscenter_vel(B) == N.z assert A.masscenter_vel(N) == N.z
def test_body_add_torque(): body = Body('body') torque_vector = body.frame.x body.apply_torque(torque_vector) assert len(body.loads) == 1 assert body.loads[0] == (body.frame, torque_vector) raises(TypeError, lambda: body.apply_torque(0))
def test_body_dcm(): A = Body('A') B = Body('B') A.frame.orient_axis(B.frame, B.frame.z, 10) assert A.dcm(B) == Matrix([[cos(10), sin(10), 0], [-sin(10), cos(10), 0], [0, 0, 1]]) assert A.dcm(B.frame) == Matrix([[cos(10), sin(10), 0], [-sin(10), cos(10), 0], [0, 0, 1]])
def test_pin_joint_chaos_pendulum(): mA, mB, lA, lB, h = symbols('mA, mB, lA, lB, h') theta, phi, omega, alpha = dynamicsymbols('theta phi omega alpha') N = ReferenceFrame('N') A = ReferenceFrame('A') B = ReferenceFrame('B') lA = (lB - h / 2) / 2 lC = (lB / 2 + h / 4) rod = Body('rod', frame=A, mass=mA) plate = Body('plate', mass=mB, frame=B) C = Body('C', frame=N) J1 = PinJoint('J1', C, rod, coordinates=theta, speeds=omega, child_joint_pos=lA * A.z, parent_axis=N.y, child_axis=A.y) J2 = PinJoint('J2', rod, plate, coordinates=phi, speeds=alpha, parent_joint_pos=lC * A.z, parent_axis=A.z, child_axis=B.z) # Check orientation assert A.dcm(N) == Matrix([[cos(theta), 0, -sin(theta)], [0, 1, 0], [sin(theta), 0, cos(theta)]]) assert A.dcm(B) == Matrix([[cos(phi), -sin(phi), 0], [sin(phi), cos(phi), 0], [0, 0, 1]]) assert B.dcm(N) == Matrix( [[cos(phi) * cos(theta), sin(phi), -sin(theta) * cos(phi)], [-sin(phi) * cos(theta), cos(phi), sin(phi) * sin(theta)], [sin(theta), 0, cos(theta)]]) # Check Angular Velocity assert A.ang_vel_in(N) == omega * N.y assert A.ang_vel_in(B) == -alpha * A.z assert N.ang_vel_in(B) == -omega * N.y - alpha * A.z # Check kde assert J1.kdes == [omega - theta.diff(t)] assert J2.kdes == [alpha - phi.diff(t)] # Check pos of masscenters assert C.masscenter.pos_from(rod.masscenter) == lA * A.z assert rod.masscenter.pos_from(plate.masscenter) == -lC * A.z # Check Linear Velocities assert rod.masscenter.vel(N) == (h / 4 - lB / 2) * omega * A.x assert plate.masscenter.vel(N) == ((h / 4 - lB / 2) * omega + (h / 4 + lB / 2) * omega) * A.x
def test_complete_simple_double_pendulum(): q1, q2 = dynamicsymbols('q1 q2') u1, u2 = dynamicsymbols('u1 u2') m, l, g = symbols('m l g') C = Body('C') # ceiling PartP = Body('P', mass=m) PartR = Body('R', mass=m) J1 = PinJoint('J1', C, PartP, speeds=u1, coordinates=q1, child_joint_pos=-l*PartP.x, parent_axis=C.z, child_axis=PartP.z) J2 = PinJoint('J2', PartP, PartR, speeds=u2, coordinates=q2, child_joint_pos=-l*PartR.x, parent_axis=PartP.z, child_axis=PartR.z) PartP.apply_force(m*g*C.x) PartR.apply_force(m*g*C.x) method = JointsMethod(C, J1, J2) method.form_eoms() assert expand(method.mass_matrix_full) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2*l**2*m*cos(q2) + 3*l**2*m, l**2*m*cos(q2) + l**2*m], [0, 0, l**2*m*cos(q2) + l**2*m, l**2*m]]) assert trigsimp(method.forcing_full) == trigsimp(Matrix([[u1], [u2], [-g*l*m*(sin(q1 + q2) + sin(q1)) - g*l*m*sin(q1) + l**2*m*(2*u1 + u2)*u2*sin(q2)], [-g*l*m*sin(q1 + q2) - l**2*m*u1**2*sin(q2)]]))
def test_chaos_pendulum(): #https://www.pydy.org/examples/chaos_pendulum.html mA, mB, lA, lB, IAxx, IBxx, IByy, IBzz, g = symbols('mA, mB, lA, lB, IAxx, IBxx, IByy, IBzz, g') theta, phi, omega, alpha = dynamicsymbols('theta phi omega alpha') A = ReferenceFrame('A') B = ReferenceFrame('B') rod = Body('rod', mass=mA, frame=A, central_inertia=inertia(A, IAxx, IAxx, 0)) plate = Body('plate', mass=mB, frame=B, central_inertia=inertia(B, IBxx, IByy, IBzz)) C = Body('C') J1 = PinJoint('J1', C, rod, coordinates=theta, speeds=omega, child_joint_pos=-lA*rod.z, parent_axis=C.y, child_axis=rod.y) J2 = PinJoint('J2', rod, plate, coordinates=phi, speeds=alpha, parent_joint_pos=(lB-lA)*rod.z, parent_axis=rod.z, child_axis=plate.z) rod.apply_force(mA*g*C.z) plate.apply_force(mB*g*C.z) method = JointsMethod(C, J1, J2) method.form_eoms() MM = method.mass_matrix forcing = method.forcing rhs = MM.LUsolve(forcing) xd = (-2 * IBxx * alpha * omega * sin(phi) * cos(phi) + 2 * IByy * alpha * omega * sin(phi) * cos(phi) - g * lA * mA * sin(theta) - g * lB * mB * sin(theta)) / (IAxx + IBxx * sin(phi)**2 + IByy * cos(phi)**2 + lA**2 * mA + lB**2 * mB) assert (rhs[0] - xd).simplify() == 0 xd = (IBxx - IByy) * omega**2 * sin(phi) * cos(phi) / IBzz assert (rhs[1] - xd).simplify() == 0
def test_simple_pedulum(): l, m, g = symbols('l m g') C = Body('C') b = Body('b', mass=m) q = dynamicsymbols('q') P = PinJoint('P', C, b, speeds=q.diff(t), coordinates=q, child_joint_pos = -l*b.x, parent_axis=C.z, child_axis=b.z) b.potential_energy = - m * g * l * cos(q) method = JointsMethod(C, P) method.form_eoms(LagrangesMethod) rhs = method.rhs() assert rhs[1] == -g*sin(q)/l
def test_pin_joint_double_pendulum(): q1, q2 = dynamicsymbols('q1 q2') u1, u2 = dynamicsymbols('u1 u2') m, l = symbols('m l') N = ReferenceFrame('N') A = ReferenceFrame('A') B = ReferenceFrame('B') C = Body('C', frame=N) # ceiling PartP = Body('P', frame=A, mass=m) PartR = Body('R', frame=B, mass=m) J1 = PinJoint('J1', C, PartP, speeds=u1, coordinates=q1, child_joint_pos=-l * A.x, parent_axis=C.frame.z, child_axis=PartP.frame.z) J2 = PinJoint('J2', PartP, PartR, speeds=u2, coordinates=q2, child_joint_pos=-l * B.x, parent_axis=PartP.frame.z, child_axis=PartR.frame.z) # Check orientation assert N.dcm(A) == Matrix([[cos(q1), -sin(q1), 0], [sin(q1), cos(q1), 0], [0, 0, 1]]) assert A.dcm(B) == Matrix([[cos(q2), -sin(q2), 0], [sin(q2), cos(q2), 0], [0, 0, 1]]) assert _simplify_matrix(N.dcm(B)) == Matrix( [[cos(q1 + q2), -sin(q1 + q2), 0], [sin(q1 + q2), cos(q1 + q2), 0], [0, 0, 1]]) # Check Angular Velocity assert A.ang_vel_in(N) == u1 * N.z assert B.ang_vel_in(A) == u2 * A.z assert B.ang_vel_in(N) == u1 * N.z + u2 * A.z # Check kde assert J1.kdes == [u1 - q1.diff(t)] assert J2.kdes == [u2 - q2.diff(t)] # Check Linear Velocity assert PartP.masscenter.vel(N) == l * u1 * A.y assert PartR.masscenter.vel(A) == l * u2 * B.y assert PartR.masscenter.vel(N) == l * u1 * A.y + l * (u1 + u2) * B.y
def test_body_add_force(): # Body with RigidBody. rigidbody_masscenter = Point('rigidbody_masscenter') rigidbody_mass = Symbol('rigidbody_mass') rigidbody_frame = ReferenceFrame('rigidbody_frame') body_inertia = inertia(rigidbody_frame, 1, 0, 0) rigid_body = Body('rigidbody_body', rigidbody_masscenter, rigidbody_mass, rigidbody_frame, body_inertia) l = Symbol('l') Fa = Symbol('Fa') point = rigid_body.masscenter.locatenew('rigidbody_body_point0', l * rigid_body.frame.x) point.set_vel(rigid_body.frame, 0) force_vector = Fa * rigid_body.frame.z # apply_force with point rigid_body.apply_force(force_vector, point) assert len(rigid_body.loads) == 1 force_point = rigid_body.loads[0][0] frame = rigid_body.frame assert force_point.vel(frame) == point.vel(frame) assert force_point.pos_from(force_point) == point.pos_from(force_point) assert rigid_body.loads[0][1] == force_vector # apply_force without point rigid_body.apply_force(force_vector) assert len(rigid_body.loads) == 2 assert rigid_body.loads[1][1] == force_vector # passing something else than point raises(TypeError, lambda: rigid_body.apply_force(force_vector, 0)) raises(TypeError, lambda: rigid_body.apply_force(0))
def test_remove_load(): P1 = Point('P1') P2 = Point('P2') B = Body('B') f1 = B.x f2 = B.y B.apply_force(f1, P1) B.apply_force(f2, P2) B.loads == [(P1, f1), (P2, f2)] B.remove_load(P2) B.loads == [(P1, f1)] B.apply_torque(f1.cross(f2)) B.loads == [(P1, f1), (B.frame, f1.cross(f2))] B.remove_load() B.loads == [(P1, f1)]
def test_jointmethod_duplicate_coordinates_speeds(): P = Body('P') C = Body('C') T = Body('T') q, u = dynamicsymbols('q u') P1 = PinJoint('P1', P, C, q) P2 = PrismaticJoint('P2', C, T, q) raises(ValueError, lambda: JointsMethod(P, P1, P2)) P1 = PinJoint('P1', P, C, speeds=u) P2 = PrismaticJoint('P2', C, T, speeds=u) raises(ValueError, lambda: JointsMethod(P, P1, P2)) P1 = PinJoint('P1', P, C, q, u) P2 = PrismaticJoint('P2', C, T, q, u) raises(ValueError, lambda: JointsMethod(P, P1, P2))
def test_custom_rigid_body(): # Body with RigidBody. rigidbody_masscenter = Point("rigidbody_masscenter") rigidbody_mass = Symbol("rigidbody_mass") rigidbody_frame = ReferenceFrame("rigidbody_frame") body_inertia = inertia(rigidbody_frame, 1, 0, 0) rigid_body = Body( "rigidbody_body", rigidbody_masscenter, rigidbody_mass, rigidbody_frame, body_inertia, ) com = rigid_body.masscenter frame = rigid_body.frame rigidbody_masscenter.set_vel(rigidbody_frame, 0) assert com.vel(frame) == rigidbody_masscenter.vel(frame) assert com.pos_from(com) == rigidbody_masscenter.pos_from(com) assert rigid_body.mass == rigidbody_mass assert rigid_body.inertia == (body_inertia, rigidbody_masscenter) assert hasattr(rigid_body, "masscenter") assert hasattr(rigid_body, "mass") assert hasattr(rigid_body, "frame") assert hasattr(rigid_body, "inertia")
def test_body_add_force(): # Body with RigidBody. rigidbody_masscenter = Point('rigidbody_masscenter') rigidbody_mass = Symbol('rigidbody_mass') rigidbody_frame = ReferenceFrame('rigidbody_frame') body_inertia = inertia(rigidbody_frame, 1, 0, 0) rigid_body = Body('rigidbody_body', rigidbody_masscenter, rigidbody_mass, rigidbody_frame, body_inertia) l = Symbol('l') Fa = Symbol('Fa') point = rigid_body.masscenter.locatenew( 'rigidbody_body_point0', l * rigid_body.frame.x) point.set_vel(rigid_body.frame, 0) force_vector = Fa * rigid_body.frame.z # apply_force with point rigid_body.apply_force(force_vector, point) assert len(rigid_body.loads) == 1 force_point = rigid_body.loads[0][0] frame = rigid_body.frame assert force_point.vel(frame) == point.vel(frame) assert force_point.pos_from(force_point) == point.pos_from(force_point) assert rigid_body.loads[0][1] == force_vector # apply_force without point rigid_body.apply_force(force_vector) assert len(rigid_body.loads) == 2 assert rigid_body.loads[1][1] == force_vector # passing something else than point raises(TypeError, lambda: rigid_body.apply_force(force_vector, 0)) raises(TypeError, lambda: rigid_body.apply_force(0))
def test_body_ang_vel(): A = Body('A') N = ReferenceFrame('N') B = Body('B', frame=N) A.frame.set_ang_vel(N, N.y) assert A.ang_vel_in(B) == N.y assert B.ang_vel_in(A) == -N.y assert A.ang_vel_in(N) == N.y
def test_jointsmethod(): P = Body('P') C = Body('C') Pin = PinJoint('P1', P, C) C_ixx, g = symbols('C_ixx g') theta, omega = dynamicsymbols('theta_P1, omega_P1') P.apply_force(g * P.y) method = JointsMethod(P, Pin) assert method.frame == P.frame assert method.bodies == [C, P] assert method.loads == [(P.masscenter, g * P.frame.y)] assert method.q == [theta] assert method.u == [omega] assert method.kdes == [omega - theta.diff()] soln = method.form_eoms() assert soln == Matrix([[-C_ixx * omega.diff()]]) assert method.forcing_full == Matrix([[omega], [0]]) assert method.mass_matrix_full == Matrix([[1, 0], [0, C_ixx]]) assert isinstance(method.method, KanesMethod)
def test_particle_body_add_force(): # Body with Particle particle_masscenter = Point('particle_masscenter') particle_mass = Symbol('particle_mass') particle_frame = ReferenceFrame('particle_frame') particle_body = Body('particle_body', particle_masscenter, particle_mass, particle_frame) a = Symbol('a') force_vector = a * particle_body.frame.x particle_body.apply_force(force_vector, particle_body.masscenter) assert len(particle_body.loads) == 1 point = particle_body.masscenter.locatenew( particle_body._name + '_point0', 0) point.set_vel(particle_body.frame, 0) force_point = particle_body.loads[0][0] frame = particle_body.frame assert force_point.vel(frame) == point.vel(frame) assert force_point.pos_from(force_point) == point.pos_from(force_point) assert particle_body.loads[0][1] == force_vector
def test_particle_body_add_force(): # Body with Particle particle_masscenter = Point('particle_masscenter') particle_mass = Symbol('particle_mass') particle_frame = ReferenceFrame('particle_frame') particle_body = Body('particle_body', particle_masscenter, particle_mass, particle_frame) a = Symbol('a') force_vector = a * particle_body.frame.x particle_body.apply_force(force_vector, particle_body.masscenter) assert len(particle_body.loads) == 1 point = particle_body.masscenter.locatenew(particle_body._name + '_point0', 0) point.set_vel(particle_body.frame, 0) force_point = particle_body.loads[0][0] frame = particle_body.frame assert force_point.vel(frame) == point.vel(frame) assert force_point.pos_from(force_point) == point.pos_from(force_point) assert particle_body.loads[0][1] == force_vector
def test_default(): body = Body('body') assert body.name == 'body' assert body.loads == [] point = Point('body_masscenter') point.set_vel(body.frame, 0) com = body.masscenter frame = body.frame assert com.vel(frame) == point.vel(frame) assert body.mass == Symbol('body_mass') ixx, iyy, izz = symbols('body_ixx body_iyy body_izz') ixy, iyz, izx = symbols('body_ixy body_iyz body_izx') assert body.inertia == (inertia(body.frame, ixx, iyy, izz, ixy, iyz, izx), body.masscenter)
def test_clear_load(): a = symbols('a') P = Point('P') B = Body('B') force = a * B.z B.apply_force(force, P) assert B.loads == [(P, force)] B.clear_loads() assert B.loads == []
def test_two_dof_joints(): q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2') m, c1, c2, k1, k2 = symbols('m c1 c2 k1 k2') W = Body('W') B1 = Body('B1', mass=m) B2 = Body('B2', mass=m) J1 = PrismaticJoint('J1', W, B1, coordinates=q1, speeds=u1) J2 = PrismaticJoint('J2', B1, B2, coordinates=q2, speeds=u2) W.apply_force(k1*q1*W.x, reaction_body=B1) W.apply_force(c1*u1*W.x, reaction_body=B1) B1.apply_force(k2*q2*W.x, reaction_body=B2) B1.apply_force(c2*u2*W.x, reaction_body=B2) method = JointsMethod(W, J1, J2) method.form_eoms() MM = method.mass_matrix forcing = method.forcing rhs = MM.LUsolve(forcing) assert expand(rhs[0]) == expand((-k1 * q1 - c1 * u1 + k2 * q2 + c2 * u2)/m) assert expand(rhs[1]) == expand((k1 * q1 + c1 * u1 - 2 * k2 * q2 - 2 * c2 * u2) / m)
def test_apply_force_multiple_one_point(): a, b = symbols('a b') P = Point('P') B = Body('B') f1 = a * B.x f2 = b * B.y B.apply_force(f1, P) assert B.loads == [(P, f1)] B.apply_force(f2, P) assert B.loads == [(P, f1 + f2)]
def test_default(): body = Body("body") assert body.name == "body" assert body.loads == [] point = Point("body_masscenter") point.set_vel(body.frame, 0) com = body.masscenter frame = body.frame assert com.vel(frame) == point.vel(frame) assert body.mass == Symbol("body_mass") ixx, iyy, izz = symbols("body_ixx body_iyy body_izz") ixy, iyz, izx = symbols("body_ixy body_iyz body_izx") assert body.inertia == ( inertia(body.frame, ixx, iyy, izz, ixy, iyz, izx), body.masscenter, )
def test_apply_torque(): t = symbols('t') q = dynamicsymbols('q') B1 = Body('B1') B2 = Body('B2') N = ReferenceFrame('N') torque = t * q * N.x B1.apply_torque(torque, B2) #Applying equal and opposite torque assert B1.loads == [(B1.frame, torque)] assert B2.loads == [(B2.frame, -torque)] torque2 = t * N.y B1.apply_torque(torque2) assert B1.loads == [(B1.frame, torque + torque2)]
def test_particle_body(): # Body with Particle particle_masscenter = Point('particle_masscenter') particle_mass = Symbol('particle_mass') particle_frame = ReferenceFrame('particle_frame') particle_body = Body('particle_body', particle_masscenter, particle_mass, particle_frame) com = particle_body.masscenter frame = particle_body.frame particle_masscenter.set_vel(particle_frame, 0) assert com.vel(frame) == particle_masscenter.vel(frame) assert com.pos_from(com) == particle_masscenter.pos_from(com) assert particle_body.mass == particle_mass assert not hasattr(particle_body, "_inertia") assert hasattr(particle_body, 'frame') assert hasattr(particle_body, 'masscenter') assert hasattr(particle_body, 'mass')
def test_custom_rigid_body(): # Body with RigidBody. rigidbody_masscenter = Point('rigidbody_masscenter') rigidbody_mass = Symbol('rigidbody_mass') rigidbody_frame = ReferenceFrame('rigidbody_frame') body_inertia = inertia(rigidbody_frame, 1, 0, 0) rigid_body = Body('rigidbody_body', rigidbody_masscenter, rigidbody_mass, rigidbody_frame, body_inertia) com = rigid_body.masscenter frame = rigid_body.frame rigidbody_masscenter.set_vel(rigidbody_frame, 0) assert com.vel(frame) == rigidbody_masscenter.vel(frame) assert com.pos_from(com) == rigidbody_masscenter.pos_from(com) assert rigid_body.mass == rigidbody_mass assert rigid_body.inertia == (body_inertia, rigidbody_masscenter) assert hasattr(rigid_body, 'masscenter') assert hasattr(rigid_body, 'mass') assert hasattr(rigid_body, 'frame') assert hasattr(rigid_body, 'inertia')
def _generate_body(): N = ReferenceFrame('N') A = ReferenceFrame('A') P = Body('P', frame=N) C = Body('C', frame=A) return N, A, P, C
def test_apply_loads_on_multi_degree_freedom_holonomic_system(): """Example based on: https://pydy.readthedocs.io/en/latest/examples/multidof-holonomic.html""" W = Body('W') #Wall B = Body('B') #Block P = Body('P') #Pendulum b = Body('b') #bob q1, q2 = dynamicsymbols('q1 q2') #generalized coordinates k, c, g, kT = symbols('k c g kT') #constants F, T = dynamicsymbols('F T') #Specified forces #Applying forces B.apply_force(F * W.x) W.apply_force(k * q1 * W.x, reaction_body=B) #Spring force W.apply_force(c * q1.diff() * W.x, reaction_body=B) #dampner P.apply_force(P.mass * g * W.y) b.apply_force(b.mass * g * W.y) #Applying torques P.apply_torque(kT * q2 * W.z, reaction_body=b) P.apply_torque(T * W.z) assert B.loads == [(B.masscenter, (F - k * q1 - c * q1.diff()) * W.x)] assert P.loads == [(P.masscenter, P.mass * g * W.y), (P.frame, (T + kT * q2) * W.z)] assert b.loads == [(b.masscenter, b.mass * g * W.y), (b.frame, -kT * q2 * W.z)] assert W.loads == [(W.masscenter, (c * q1.diff() + k * q1) * W.x)]
def test_Joint(): parent = Body('parent') child = Body('child') raises(TypeError, lambda: Joint('J', parent, child))
def test_apply_force(): f, g = symbols('f g') q, x, v1, v2 = dynamicsymbols('q x v1 v2') P1 = Point('P1') P2 = Point('P2') B1 = Body('B1') B2 = Body('B2') N = ReferenceFrame('N') P1.set_vel(B1.frame, v1 * B1.x) P2.set_vel(B2.frame, v2 * B2.x) force = f * q * N.z # time varying force B1.apply_force(force, P1, B2, P2) #applying equal and opposite force on moving points assert B1.loads == [(P1, force)] assert B2.loads == [(P2, -force)] g1 = B1.mass * g * N.y g2 = B2.mass * g * N.y B1.apply_force(g1) #applying gravity on B1 masscenter B2.apply_force(g2) #applying gravity on B2 masscenter assert B1.loads == [(P1, force), (B1.masscenter, g1)] assert B2.loads == [(P2, -force), (B2.masscenter, g2)] force2 = x * N.x B1.apply_force( force2, reaction_body=B2) #Applying time varying force on masscenter assert B1.loads == [(P1, force), (B1.masscenter, force2 + g1)] assert B2.loads == [(P2, -force), (B2.masscenter, -force2 + g2)]
def test_body_axis(): N = ReferenceFrame('N') B = Body('B', frame=N) assert B.x == N.x assert B.y == N.y assert B.z == N.z