def test_point_funcs():
q, q2 = dynamicsymbols("q q2")
qd, q2d = dynamicsymbols("q q2", 1)
qdd, q2dd = dynamicsymbols("q q2", 2)
N = ReferenceFrame("N")
B = ReferenceFrame("B")
B.set_ang_vel(N, 5 * B.y)
O = Point("O")
P = O.locatenew("P", q * B.x)
assert P.pos_from(O) == q * B.x
P.set_vel(B, qd * B.x + q2d * B.y)
assert P.vel(B) == qd * B.x + q2d * B.y
O.set_vel(N, 0)
assert O.vel(N) == 0
assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
(-10 * qd) * B.z)
B = N.orientnew("B", "Axis", [q, N.z])
O = Point("O")
P = O.locatenew("P", 10 * B.x)
O.set_vel(N, 5 * N.x)
assert O.vel(N) == 5 * N.x
assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
B.set_ang_vel(N, 5 * B.y)
O = Point("O")
P = O.locatenew("P", q * B.x)
P.set_vel(B, qd * B.x + q2d * B.y)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
def test_point_funcs():
q, q2 = dynamicsymbols('q q2')
qd, q2d = dynamicsymbols('q q2', 1)
qdd, q2dd = dynamicsymbols('q q2', 2)
N = ReferenceFrame('N')
B = ReferenceFrame('B')
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
assert P.pos_from(O) == q * B.x
P.set_vel(B, qd * B.x + q2d * B.y)
assert P.vel(B) == qd * B.x + q2d * B.y
O.set_vel(N, 0)
assert O.vel(N) == 0
assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
(-10 * qd) * B.z)
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 10 * B.x)
O.set_vel(N, 5 * N.x)
assert O.vel(N) == 5 * N.x
assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
P.set_vel(B, qd * B.x + q2d * B.y)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
def test_auto_vel_derivative():
q1, q2 = dynamicsymbols('q1:3')
u1, u2 = dynamicsymbols('u1:3', 1)
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
B.orient_axis(A, A.z, q1)
B.set_ang_vel(A, u1 * A.z)
C.orient_axis(B, B.z, q2)
C.set_ang_vel(B, u2 * B.z)
Am = Point('Am')
Am.set_vel(A, 0)
Bm = Point('Bm')
Bm.set_pos(Am, B.x)
Bm.set_vel(B, 0)
Bm.set_vel(C, 0)
Cm = Point('Cm')
Cm.set_pos(Bm, C.x)
Cm.set_vel(C, 0)
temp = Cm._vel_dict.copy()
assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
Cm._vel_dict = temp
Cm.v2pt_theory(Bm, B, C)
assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
def test_point_funcs():
q, q2 = dynamicsymbols('q q2')
qd, q2d = dynamicsymbols('q q2', 1)
qdd, q2dd = dynamicsymbols('q q2', 2)
N = ReferenceFrame('N')
B = ReferenceFrame('B')
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
assert P.pos_from(O) == q * B.x
P.set_vel(B, qd * B.x + q2d * B.y)
assert P.vel(B) == qd * B.x + q2d * B.y
O.set_vel(N, 0)
assert O.vel(N) == 0
assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
(-10 * qd) * B.z)
B = N.orientnew('B', 'Axis', [q, N.z])
O = Point('O')
P = O.locatenew('P', 10 * B.x)
O.set_vel(N, 5 * N.x)
assert O.vel(N) == 5 * N.x
assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
B.set_ang_vel(N, 5 * B.y)
O = Point('O')
P = O.locatenew('P', q * B.x)
P.set_vel(B, qd * B.x + q2d * B.y)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
def test_point_funcs():
q, q2 = dynamicsymbols("q q2")
qd, q2d = dynamicsymbols("q q2", 1)
qdd, q2dd = dynamicsymbols("q q2", 2)
N = ReferenceFrame("N")
B = ReferenceFrame("B")
B.set_ang_vel(N, 5 * B.y)
O = Point("O")
P = O.locatenew("P", q * B.x)
assert P.pos_from(O) == q * B.x
P.set_vel(B, qd * B.x + q2d * B.y)
assert P.vel(B) == qd * B.x + q2d * B.y
O.set_vel(N, 0)
assert O.vel(N) == 0
assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y + (-10 * qd) * B.z)
B = N.orientnew("B", "Axis", [q, N.z])
O = Point("O")
P = O.locatenew("P", 10 * B.x)
O.set_vel(N, 5 * N.x)
assert O.vel(N) == 5 * N.x
assert P.a2pt_theory(O, N, B) == (-10 * qd ** 2) * B.x + (10 * qdd) * B.y
B.set_ang_vel(N, 5 * B.y)
O = Point("O")
P = O.locatenew("P", q * B.x)
P.set_vel(B, qd * B.x + q2d * B.y)
O.set_vel(N, 0)
assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
def test_point_vel(): #Basic functionality
q1, q2 = dynamicsymbols('q1 q2')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
Q = Point('Q')
O = Point('O')
Q.set_pos(O, q1 * N.x)
raises(ValueError, lambda: Q.vel(N)) # Velocity of O in N is not defined
O.set_vel(N, q2 * N.y)
assert O.vel(N) == q2 * N.y
raises(ValueError, lambda: O.vel(B)) #Velocity of O is not defined in B
def test_auto_point_vel_if_tree_has_vel_but_inappropriate_pos_vector():
q1, q2 = dynamicsymbols('q1 q2')
B = ReferenceFrame('B')
S = ReferenceFrame('S')
P = Point('P')
P.set_vel(B, q1 * B.x)
P1 = Point('P1')
P1.set_pos(P, S.y)
raises(ValueError,
lambda: P1.vel(B)) # P1.pos_from(P) can't be expressed in B
raises(ValueError, lambda: P1.vel(S)) # P.vel(S) not defined
def test_auto_vel_dont_overwrite():
t = dynamicsymbols._t
q1, q2, u1 = dynamicsymbols('q1, q2, u1')
N = ReferenceFrame('N')
P = Point('P1')
P.set_vel(N, u1 * N.x)
P1 = Point('P1')
P1.set_pos(P, q2 * N.y)
assert P1.vel(N) == q2.diff(t) * N.y + u1 * N.x
assert P.vel(N) == u1 * N.x
P1.set_vel(N, u1 * N.z)
assert P1.vel(N) == u1 * N.z
def test_auto_point_vel_connected_frames():
t = dynamicsymbols._t
q, q1, q2, u = dynamicsymbols('q q1 q2 u')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
O = Point('O')
O.set_vel(N, u * N.x)
P = Point('P')
P.set_pos(O, q1 * N.x + q2 * B.y)
raises(ValueError, lambda: P.vel(N))
N.orient(B, 'Axis', (q, B.x))
assert P.vel(
N) == (u + q1.diff(t)) * N.x + q2.diff(t) * B.y - q2 * q.diff(t) * B.z
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_partial_velocity():
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
u4, u5 = dynamicsymbols('u4, u5')
r = symbols('r')
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
C = Point('C')
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
u_list = [u1, u2, u3, u4, u5]
assert (partial_velocity(vel_list, u_list, N) == [[
-r * L.y, r * L.x, 0, L.x,
cos(q2) * L.y - sin(q2) * L.z
], [0, 0, 0, L.x, cos(q2) * L.y - sin(q2) * L.z], [L.x, L.y, L.z, 0, 0]])
# Make sure that partial velocities can be computed regardless if the
# orientation between frames is defined or not.
A = ReferenceFrame('A')
B = ReferenceFrame('B')
v = u4 * A.x + u5 * B.y
assert partial_velocity((v, ), (u4, u5), A) == [[A.x, B.y]]
raises(TypeError, lambda: partial_velocity(Dmc.vel(N), u_list, N))
raises(TypeError, lambda: partial_velocity(vel_list, u1, N))
def test_auto_point_vel_shortest_path():
t = dynamicsymbols._t
q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
B = ReferenceFrame('B')
P = Point('P')
P.set_vel(B, u1 * B.x)
P1 = Point('P1')
P1.set_pos(P, q2 * B.y)
P1.set_vel(B, q1 * B.z)
P2 = Point('P2')
P2.set_pos(P1, q1 * B.z)
P3 = Point('P3')
P3.set_pos(P2, 10 * q1 * B.y)
P4 = Point('P4')
P4.set_pos(P3, q1 * B.x)
O = Point('O')
O.set_vel(B, u2 * B.y)
O1 = Point('O1')
O1.set_pos(O, q2 * B.z)
P4.set_pos(O1, q1 * B.x + q2 * B.z)
with warnings.catch_warnings(
): #There are two possible paths in this point tree, thus a warning is raised
warnings.simplefilter('error')
with ignore_warnings(UserWarning):
assert P4.vel(
B) == q1.diff(t) * B.x + u2 * B.y + 2 * q2.diff(t) * B.z
def test_partial_velocity():
q1, q2, q3, u1, u2, u3 = dynamicsymbols("q1 q2 q3 u1 u2 u3")
u4, u5 = dynamicsymbols("u4, u5")
r = symbols("r")
N = ReferenceFrame("N")
Y = N.orientnew("Y", "Axis", [q1, N.z])
L = Y.orientnew("L", "Axis", [q2, Y.x])
R = L.orientnew("R", "Axis", [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
C = Point("C")
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew("Dmc", r * L.z)
Dmc.v2pt_theory(C, N, R)
vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
u_list = [u1, u2, u3, u4, u5]
assert partial_velocity(vel_list, u_list, N) == [
[-r * L.y, r * L.x, 0, L.x,
cos(q2) * L.y - sin(q2) * L.z],
[0, 0, 0, L.x, cos(q2) * L.y - sin(q2) * L.z],
[L.x, L.y, L.z, 0, 0],
]
# Make sure that partial velocities can be computed regardless if the
# orientation between frames is defined or not.
A = ReferenceFrame("A")
B = ReferenceFrame("B")
v = u4 * A.x + u5 * B.y
assert partial_velocity((v, ), (u4, u5), A) == [[A.x, B.y]]
raises(TypeError, lambda: partial_velocity(Dmc.vel(N), u_list, N))
raises(TypeError, lambda: partial_velocity(vel_list, u1, N))
def test_partial_velocity():
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
u4, u5 = dynamicsymbols('u4, u5')
r = symbols('r')
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
C = Point('C')
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
u_list = [u1, u2, u3, u4, u5]
assert (partial_velocity(vel_list, u_list, N) ==
[[- r*L.y, r*L.x, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
[0, 0, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
[L.x, L.y, L.z, 0, 0]])
# Make sure that partial velocities can be computed regardless if the
# orientation between frames is defined or not.
A = ReferenceFrame('A')
B = ReferenceFrame('B')
v = u4 * A.x + u5 * B.y
assert partial_velocity((v, ), (u4, u5), A) == [[A.x, B.y]]
raises(TypeError, lambda: partial_velocity(Dmc.vel(N), u_list, N))
raises(TypeError, lambda: partial_velocity(vel_list, u1, N))
def test_auto_point_vel():
t = dynamicsymbols._t
q1, q2 = dynamicsymbols('q1 q2')
N = ReferenceFrame('N')
B = ReferenceFrame('B')
O = Point('O')
Q = Point('Q')
Q.set_pos(O, q1 * N.x)
O.set_vel(N, q2 * N.y)
assert Q.vel(N) == q1.diff(t) * N.x + q2 * N.y # Velocity of Q using O
P1 = Point('P1')
P1.set_pos(O, q1 * B.x)
P2 = Point('P2')
P2.set_pos(P1, q2 * B.z)
raises(ValueError, lambda: P2.vel(B)
) # O's velocity is defined in different frame, and no
#point in between has its velocity defined
raises(ValueError, lambda: P2.vel(N)) # Velocity of O not defined in N
def test_auto_vel_multiple_path_warning_msg():
N = ReferenceFrame('N')
O = Point('O')
P = Point('P')
Q = Point('Q')
P.set_vel(N, N.x)
Q.set_vel(N, N.y)
O.set_pos(P, N.z)
O.set_pos(Q, N.y)
with warnings.catch_warnings(
record=True
) as w: #There are two possible paths in this point tree, thus a warning is raised
warnings.simplefilter("always")
O.vel(N)
assert issubclass(w[-1].category, UserWarning)
assert 'Velocity automatically calculated based on point' in str(
w[-1].message)
assert 'Velocities from these points are not necessarily the same. This may cause errors in your calculations.' in str(
w[-1].message)
def test_auto_vel_cyclic_warning_msg():
P = Point('P')
P1 = Point('P1')
P2 = Point('P2')
P3 = Point('P3')
N = ReferenceFrame('N')
P.set_vel(N, N.x)
P1.set_pos(P, N.x)
P2.set_pos(P1, N.y)
P3.set_pos(P2, N.z)
P1.set_pos(P3, N.x + N.y)
with warnings.catch_warnings(
record=True
) as w: #The path is cyclic at P1, thus a warning is raised
warnings.simplefilter("always")
P2.vel(N)
assert issubclass(w[-1].category, UserWarning)
assert 'Kinematic loops are defined among the positions of points. This is likely not desired and may cause errors in your calculations.' in str(
w[-1].message)
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_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_auto_point_vel_multiple_point_path():
t = dynamicsymbols._t
q1, q2 = dynamicsymbols('q1 q2')
B = ReferenceFrame('B')
P = Point('P')
P.set_vel(B, q1 * B.x)
P1 = Point('P1')
P1.set_pos(P, q2 * B.y)
P1.set_vel(B, q1 * B.z)
P2 = Point('P2')
P2.set_pos(P1, q1 * B.z)
P3 = Point('P3')
P3.set_pos(P2, 10 * q1 * B.y)
assert P3.vel(B) == 10 * q1.diff(t) * B.y + (q1 + q1.diff(t)) * B.z
def test_auto_vel_cyclic_warning_arises():
P = Point('P')
P1 = Point('P1')
P2 = Point('P2')
P3 = Point('P3')
N = ReferenceFrame('N')
P.set_vel(N, N.x)
P1.set_pos(P, N.x)
P2.set_pos(P1, N.y)
P3.set_pos(P2, N.z)
P1.set_pos(P3, N.x + N.y)
with warnings.catch_warnings(
): #The path is cyclic at P1, thus a warning is raised
warnings.simplefilter("error")
raises(UserWarning, lambda: P2.vel(N))
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_auto_point_vel_multiple_paths_warning_arises():
q, u = dynamicsymbols('q u')
N = ReferenceFrame('N')
O = Point('O')
P = Point('P')
Q = Point('Q')
R = Point('R')
P.set_vel(N, u * N.x)
Q.set_vel(N, u * N.y)
R.set_vel(N, u * N.z)
O.set_pos(P, q * N.z)
O.set_pos(Q, q * N.y)
O.set_pos(R, q * N.x)
with warnings.catch_warnings(
): #There are two possible paths in this point tree, thus a warning is raised
warnings.simplefilter("error")
raises(UserWarning, lambda: O.vel(N))
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_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 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_partial_velocity():
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
u4, u5 = dynamicsymbols('u4, u5')
r = symbols('r')
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
C = Point('C')
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
u_list = [u1, u2, u3, u4, u5]
assert (partial_velocity(vel_list, u_list, N) ==
[[- r*L.y, r*L.x, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
[0, 0, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
[L.x, L.y, L.z, 0, 0]])
def test_partial_velocity():
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
u4, u5 = dynamicsymbols('u4, u5')
r = symbols('r')
N = ReferenceFrame('N')
Y = N.orientnew('Y', 'Axis', [q1, N.z])
L = Y.orientnew('L', 'Axis', [q2, Y.x])
R = L.orientnew('R', 'Axis', [q3, L.y])
R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
C = Point('C')
C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
Dmc = C.locatenew('Dmc', r * L.z)
Dmc.v2pt_theory(C, N, R)
vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
u_list = [u1, u2, u3, u4, u5]
assert (partial_velocity(vel_list, u_list, N) == [[
-r * L.y, r * L.x, 0, L.x,
cos(q2) * L.y - sin(q2) * L.z
], [0, 0, 0, L.x, cos(q2) * L.y - sin(q2) * L.z], [L.x, L.y, L.z, 0, 0]])
