def test_orient_new_methods():
N = CoordSysCartesian('N')
D = N.orient_new('D', 'Axis', [q4, N.j])
E = N.orient_new('E', 'Space', [q1, q2, q3], '123')
F = N.orient_new('F', 'Quaternion', [q1, q2, q3, q4])
G = N.orient_new('G', 'Body', [q1, q2, q3], '123')
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_orient_new_methods():
N = CoordSysCartesian('N')
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, '123')
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, '123')
D = N.orient_new('D', (orienter1, ))
E = N.orient_new('E', (orienter2, ))
F = N.orient_new('F', (orienter3, ))
G = N.orient_new('G', (orienter4, ))
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_orient_new_methods():
N = CoordSysCartesian("N")
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, "123")
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, "123")
D = N.orient_new("D", (orienter1,))
E = N.orient_new("E", (orienter2,))
F = N.orient_new("F", (orienter3,))
G = N.orient_new("G", (orienter4,))
assert D == N.orient_new_axis("D", q4, N.j)
assert E == N.orient_new_space("E", q1, q2, q3, "123")
assert F == N.orient_new_quaternion("F", q1, q2, q3, q4)
assert G == N.orient_new_body("G", q1, q2, q3, "123")
def test_orient_new_methods():
N = CoordSysCartesian('N')
orienter1 = AxisOrienter(q4, N.j)
orienter2 = SpaceOrienter(q1, q2, q3, '123')
orienter3 = QuaternionOrienter(q1, q2, q3, q4)
orienter4 = BodyOrienter(q1, q2, q3, '123')
D = N.orient_new('D', (orienter1, ))
E = N.orient_new('E', (orienter2, ))
F = N.orient_new('F', (orienter3, ))
G = N.orient_new('G', (orienter4, ))
assert D == N.orient_new_axis('D', q4, N.j)
assert E == N.orient_new_space('E', q1, q2, q3, '123')
assert F == N.orient_new_quaternion('F', q1, q2, q3, q4)
assert G == N.orient_new_body('G', q1, q2, q3, '123')
def test_rotation_matrix():
N = CoordSysCartesian('N')
A = N.orient_new('A', 'Axis', [q1, N.k])
B = A.orient_new('B', 'Axis', [q2, A.i])
C = B.orient_new('C', 'Axis', [q3, B.j])
D = N.orient_new('D', 'Axis', [q4, N.j])
E = N.orient_new('E', 'Space', [q1, q2, q3], '123')
F = N.orient_new('F', 'Quaternion', [q1, q2, q3, q4])
G = N.orient_new('G', 'Body', [q1, q2, q3], '123')
assert N.rotation_matrix(C) == Matrix([
[- sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), - sin(q1) *
cos(q2), sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), \
cos(q1) * cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * \
cos(q3)], [- sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]])
test_mat = D.rotation_matrix(C) - Matrix(
[[cos(q1) * cos(q3) * cos(q4) - sin(q3) * (- sin(q4) * cos(q2) +
sin(q1) * sin(q2) * cos(q4)), - sin(q2) * sin(q4) - sin(q1) *
cos(q2) * cos(q4), sin(q3) * cos(q1) * cos(q4) + cos(q3) * \
(- sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4))], \
[sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * \
cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)], \
[sin(q4) * cos(q1) * cos(q3) - sin(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * \
sin(q4)), sin(q2) *
cos(q4) - sin(q1) * sin(q4) * cos(q2), sin(q3) * \
sin(q4) * cos(q1) + cos(q3) * (cos(q2) * cos(q4) + \
sin(q1) * sin(q2) * sin(q4))]])
assert test_mat.expand() == zeros(3, 3)
assert E.rotation_matrix(N) == Matrix(
[[cos(q2)*cos(q3), sin(q3)*cos(q2), -sin(q2)],
[sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1), \
sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2)], \
[sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), - \
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2)]])
assert F.rotation_matrix(N) == Matrix([[
q1**2 + q2**2 - q3**2 - q4**2,
2*q1*q4 + 2*q2*q3, -2*q1*q3 + 2*q2*q4],[ -2*q1*q4 + 2*q2*q3,
q1**2 - q2**2 + q3**2 - q4**2, 2*q1*q2 + 2*q3*q4],
[2*q1*q3 + 2*q2*q4,
-2*q1*q2 + 2*q3*q4,
q1**2 - q2**2 - q3**2 + q4**2]])
assert G.rotation_matrix(N) == Matrix([[
cos(q2)*cos(q3), sin(q1)*sin(q2)*cos(q3) + sin(q3)*cos(q1),
sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3)], [
-sin(q3)*cos(q2), -sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3),
sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],[
sin(q2), -sin(q1)*cos(q2), cos(q1)*cos(q2)]])
from sympy.vector.vector import Vector
from sympy.vector.coordsysrect import CoordSysCartesian
from sympy.vector.functions import express, matrix_to_vector
from sympy import symbols, S, sin, cos, ImmutableMatrix as Matrix
N = CoordSysCartesian('N')
q1, q2, q3, q4, q5 = symbols('q1 q2 q3 q4 q5')
A = N.orient_new('A', 'Axis', [q1, N.k])
B = A.orient_new('B', 'Axis', [q2, A.i])
C = B.orient_new('C', 'Axis', [q3, B.j])
def test_express():
assert express(Vector.zero, N) == Vector.zero
assert express(S(0), N) == S(0)
assert express(A.i, C) == cos(q3) * C.i + sin(q3) * C.k
assert express(A.j, C) == sin(q2)*sin(q3)*C.i + cos(q2)*C.j - \
sin(q2)*cos(q3)*C.k
assert express(A.k, C) == -sin(q3)*cos(q2)*C.i + sin(q2)*C.j + \
cos(q2)*cos(q3)*C.k
assert express(A.i, N) == cos(q1) * N.i + sin(q1) * N.j
assert express(A.j, N) == -sin(q1) * N.i + cos(q1) * N.j
assert express(A.k, N) == N.k
assert express(A.i, A) == A.i
assert express(A.j, A) == A.j
assert express(A.k, A) == A.k
assert express(A.i, B) == B.i
assert express(A.j, B) == cos(q2) * B.j - sin(q2) * B.k
assert express(A.k, B) == sin(q2) * B.j + cos(q2) * B.k
assert express(A.i, C) == cos(q3) * C.i + sin(q3) * C.k
assert express(A.j, C) == sin(q2)*sin(q3)*C.i + cos(q2)*C.j - \
def test_vector():
"""
Tests the effects of orientation of coordinate systems on
basic vector operations.
"""
N = CoordSysCartesian('N')
A = N.orient_new('A', 'Axis', [q1, N.k])
B = A.orient_new('B', 'Axis', [q2, A.i])
C = B.orient_new('C', 'Axis', [q3, B.j])
#Test to_matrix
v1 = a*N.i + b*N.j + c*N.k
assert v1.to_matrix(A) == Matrix([[ a*cos(q1) + b*sin(q1)],
[-a*sin(q1) + b*cos(q1)],
[ c]])
#Test dot
assert N.i.dot(A.i) == cos(q1)
assert N.i.dot(A.j) == -sin(q1)
assert N.i.dot(A.k) == 0
assert N.j.dot(A.i) == sin(q1)
assert N.j.dot(A.j) == cos(q1)
assert N.j.dot(A.k) == 0
assert N.k.dot(A.i) == 0
assert N.k.dot(A.j) == 0
assert N.k.dot(A.k) == 1
assert N.i.dot(A.i + A.j) == -sin(q1) + cos(q1) == \
(A.i + A.j).dot(N.i)
assert A.i.dot(C.i) == cos(q3)
assert A.i.dot(C.j) == 0
assert A.i.dot(C.k) == sin(q3)
assert A.j.dot(C.i) == sin(q2)*sin(q3)
assert A.j.dot(C.j) == cos(q2)
assert A.j.dot(C.k) == -sin(q2)*cos(q3)
assert A.k.dot(C.i) == -cos(q2)*sin(q3)
assert A.k.dot(C.j) == sin(q2)
assert A.k.dot(C.k) == cos(q2)*cos(q3)
#Test cross
assert N.i.cross(A.i) == sin(q1)*A.k
assert N.i.cross(A.j) == cos(q1)*A.k
assert N.i.cross(A.k) == -sin(q1)*A.i - cos(q1)*A.j
assert N.j.cross(A.i) == -cos(q1)*A.k
assert N.j.cross(A.j) == sin(q1)*A.k
assert N.j.cross(A.k) == cos(q1)*A.i - sin(q1)*A.j
assert N.k.cross(A.i) == A.j
assert N.k.cross(A.j) == -A.i
assert N.k.cross(A.k) == Vector.zero
assert N.i.cross(A.i) == sin(q1)*A.k
assert N.i.cross(A.j) == cos(q1)*A.k
assert N.i.cross(A.i + A.j) == sin(q1)*A.k + cos(q1)*A.k
assert (A.i + A.j).cross(N.i) == (-sin(q1) - cos(q1))*N.k
assert A.i.cross(C.i) == sin(q3)*C.j
assert A.i.cross(C.j) == -sin(q3)*C.i + cos(q3)*C.k
assert A.i.cross(C.k) == -cos(q3)*C.j
assert C.i.cross(A.i) == (-sin(q3)*cos(q2))*A.j + \
(-sin(q2)*sin(q3))*A.k
assert C.j.cross(A.i) == (sin(q2))*A.j + (-cos(q2))*A.k
assert express(C.k.cross(A.i), C).trigsimp() == cos(q3)*C.j
