def test_orient_body():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
B.orient_body_fixed(A, (1, 1, 0), 'XYX')
assert B.dcm(A) == Matrix([[cos(1), sin(1)**2, -sin(1) * cos(1)],
[0, cos(1), sin(1)],
[sin(1), -sin(1) * cos(1),
cos(1)**2]])
def test_orient_body_simple_ang_vel():
"""orient_body_fixed() uses kinematic_equations() internally and solves
those equations for the measure numbers of the angular velocity. This test
ensures that the simplest form of that linear system solution is returned,
thus the == for the expression comparison."""
psi, theta, phi = dynamicsymbols('psi, theta, varphi')
t = dynamicsymbols._t
A = ReferenceFrame('A')
B = ReferenceFrame('B')
B.orient_body_fixed(A, (psi, theta, phi), 'ZXZ')
A_w_B = B.ang_vel_in(A)
assert A_w_B.args[0][1] == B
assert A_w_B.args[0][0][0] == (sin(theta) * sin(phi) * psi.diff(t) +
cos(phi) * theta.diff(t))
assert A_w_B.args[0][0][1] == (sin(theta) * cos(phi) * psi.diff(t) -
sin(phi) * theta.diff(t))
assert A_w_B.args[0][0][2] == cos(theta) * psi.diff(t) + phi.diff(t)
