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_vector_angle():
A = ReferenceFrame('A')
v1 = A.x + A.y
v2 = A.z
assert v1.angle_between(v2) == pi/2
B = ReferenceFrame('B')
B.orient_axis(A, A.x, pi)
v3 = A.x
v4 = B.x
assert v3.angle_between(v4) == 0
def test_orient_axis():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
A.orient_axis(B, -B.x, 1)
A1 = A.dcm(B)
A.orient_axis(B, B.x, -1)
A2 = A.dcm(B)
A.orient_axis(B, 1, -B.x)
A3 = A.dcm(B)
assert A1 == A2
assert A2 == A3
raises(TypeError, lambda: A.orient_axis(B, 1, 1))
def test_dcm_cache_dict():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
D = ReferenceFrame('D')
a, b, c = symbols('a b c')
B.orient_axis(A, A.x, a)
C.orient_axis(B, B.x, b)
D.orient_axis(C, C.x, c)
assert D._dcm_dict == {
C: Matrix([[1, 0, 0], [0, cos(c), sin(c)], [0, -sin(c),
cos(c)]])
}
assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]]), \
D: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c), cos(c)]])}
assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0, cos(a), sin(a)],[0, -sin(a), cos(a)]]), \
C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])}
assert A._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(a), -sin(a)], [0, sin(a),
cos(a)]])
}
assert D._dcm_dict == D._dcm_cache
D.dcm(
A
) # Check calculated dcm relation is stored in _dcm_cache and not in _dcm_dict
assert list(A._dcm_cache.keys()) == [A, B, D]
assert list(D._dcm_cache.keys()) == [C, A]
assert list(A._dcm_dict.keys()) == [B]
assert list(D._dcm_dict.keys()) == [C]
assert A._dcm_dict != A._dcm_cache
A.orient_axis(
B, B.x, b) # _dcm_cache of A is wiped out and new relation is stored.
assert A._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(b), sin(b)], [0, -sin(b),
cos(b)]])
}
assert A._dcm_dict == A._dcm_cache
assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]]), \
A: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])}
def test_looped_frame_warning():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
a, b, c = symbols('a b c')
B.orient_axis(A, A.x, a)
C.orient_axis(B, B.x, b)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
A.orient_axis(C, C.x, c)
assert issubclass(w[-1].category, UserWarning)
assert 'Loops are defined among the orientation of frames. ' + \
'This is likely not desired and may cause errors in your calculations.' in str(w[-1].message)
def test_dict_list():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
D = ReferenceFrame('D')
E = ReferenceFrame('E')
F = ReferenceFrame('F')
B.orient_axis(A, A.x, 1.0)
C.orient_axis(B, B.x, 1.0)
D.orient_axis(C, C.x, 1.0)
assert D._dict_list(A, 0) == [D, C, B, A]
E.orient_axis(D, D.x, 1.0)
assert C._dict_list(A, 0) == [C, B, A]
assert C._dict_list(E, 0) == [C, D, E]
# only 0, 1, 2 permitted for second argument
raises(ValueError, lambda: C._dict_list(E, 5))
# no connecting path
raises(ValueError, lambda: F._dict_list(A, 0))
def test_frame_dict():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
C = ReferenceFrame('C')
a, b, c = symbols('a b c')
B.orient_axis(A, A.x, a)
assert A._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(a), -sin(a)], [0, sin(a),
cos(a)]])
}
assert B._dcm_dict == {
A: Matrix([[1, 0, 0], [0, cos(a), sin(a)], [0, -sin(a),
cos(a)]])
}
assert C._dcm_dict == {}
B.orient_axis(C, C.x, b)
# Previous relation is not wiped
assert A._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(a), -sin(a)], [0, sin(a),
cos(a)]])
}
assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0, cos(a), sin(a)],[0, -sin(a), cos(a)]]), \
C: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]])}
assert C._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(b), -sin(b)], [0, sin(b),
cos(b)]])
}
A.orient_axis(B, B.x, c)
# Previous relation is updated
assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]]),\
A: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c), cos(c)]])}
assert A._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(c), sin(c)], [0, -sin(c),
cos(c)]])
}
assert C._dcm_dict == {
B: Matrix([[1, 0, 0], [0, cos(b), -sin(b)], [0, sin(b),
cos(b)]])
}
def test_orient_axis():
A = ReferenceFrame('A')
B = ReferenceFrame('B')
assert A.orient_axis(B, -B.x, 1) == A.orient_axis(B, B.x, -1)
