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from sympy.core.backend import Symbol, symbols, sin, cos, Matrixfrom sympy.physics.vector import Point, ReferenceFrame, dynamicsymbolsfrom sympy.physics.mechanics import inertia, Bodyfrom sympy.testing.pytest import raises
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_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 rigid_body.is_rigidbody
assert hasattr(rigid_body, 'masscenter') assert hasattr(rigid_body, 'mass') assert hasattr(rigid_body, 'frame') assert hasattr(rigid_body, 'inertia')
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')
assert not particle_body.is_rigidbody
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_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_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_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_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_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_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
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_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_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_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_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) assert B.loads == [(P1, f1), (P2, f2)] B.remove_load(P2) assert B.loads == [(P1, f1)] B.apply_torque(f1.cross(f2)) assert B.loads == [(P1, f1), (B.frame, f1.cross(f2))] B.remove_load() assert B.loads == [(P1, f1)]
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)]
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