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_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_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_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_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_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_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_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_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_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
