def test_rotations(self):
assert_aae(rotations(('z', pi / 2)),
[[0, -1, 0], [1, 0, 0], [0, 0, 1]])
# Work these two examples out by hand: apply the rotations in
# turn about the updated axes, and see where the body axes end
# up pointing.
assert_aae(rotations(('z', pi / 2), ('x', pi / 2)),
[[0, 0, 1], [1, 0, 0], [0, 1, 0]])
assert_aae(rotations(('z', pi / 2), ('x', pi / 2), ('z', pi / 2)),
[[0, 0, 1], [0, -1, 0], [1, 0, 0]])
assert_aae(rotations(('x', pi / 2), ('z', pi / 2)),
[[0, -1, 0], [0, 0, -1], [1, 0, 0]])
def test_three_rigid_elements_as_disc_have_ends_in_right_place(self):
length = 20.0
offset = 5.0
# Make 3 elements spaced by 120 deg about z axis
system = System()
elements = []
for i in range(3):
rotmat = rotations(('z', i * 2*pi/3))
offset_vector = dot(rotmat, [offset, 0, 0])
conn = RigidConnection('offset%d' % i, offset_vector, rotmat)
element = RigidConnection('element%d' % i, [length, 0, 0])
elements.append(element)
system.add_leaf(conn)
conn.add_leaf(element)
system.setup()
r = offset
R = offset + length
assert_aae(elements[0].rp, [r, 0, 0])
assert_aae(elements[1].rp, [-r/2, r*sqrt(3)/2, 0])
assert_aae(elements[2].rp, [-r/2, -r*sqrt(3)/2, 0])
assert_aae(elements[0].rd, [R, 0, 0])
assert_aae(elements[1].rd, [-R/2, R*sqrt(3)/2, 0])
assert_aae(elements[2].rd, [-R/2, -R*sqrt(3)/2, 0])
def test_rotations(self):
assert_aae(rotations(('z', pi/2)),
[[0, -1, 0],
[1, 0, 0],
[0, 0, 1]])
# Work these two examples out by hand: apply the rotations in
# turn about the updated axes, and see where the body axes end
# up pointing.
assert_aae(rotations(('z', pi/2), ('x', pi/2)),
[[0, 0, 1],
[1, 0, 0],
[0, 1, 0]])
assert_aae(rotations(('z', pi/2), ('x', pi/2), ('z', pi/2)),
[[0, 0, 1],
[0, -1, 0],
[1, 0, 0]])
assert_aae(rotations(('x', pi/2), ('z', pi/2)),
[[0, -1, 0],
[0, 0, -1],
[1, 0, 0]])
def test_three_elements_forming_a_disc_about_X_have_correct_inertia(self):
density = 5
length = 20.0
offset = 1.25
m = density * length # mass of one beam
joint = FreeJoint('joint')
# Make 3 elements spaced by 120 deg about z axis
for i in range(3):
# Rotation of -pi/2 about y aligns local x axis of ModalElement
rotmat = rotations(('x', i * 2*pi/3), ('y', -pi/2))
offset_vector = dot(rotmat, [offset, 0, 0]) # offset // local x
conn = RigidConnection('offset%d' % i, offset_vector, rotmat)
element = _mock_rigid_uniform_beam(density, length,
'element%d' % i)
joint.add_leaf(conn)
conn.add_leaf(element)
system = System()
system.add_leaf(joint)
system.setup()
# Calculate reduced system to get rigid body matrices
rsys = ReducedSystem(system)
# Expected values: perp inertia using projected lengths of beams
Iy = m * (length**2 / 12 + (length/2 + offset)**2)
Iperp = Iy + Iy/4 + Iy/4
Iaxial = 3 * Iy
expected_mass = 3 * m * eye(3)
expected_inertia = diag([Iaxial, Iperp, Iperp])
expected_offdiag = zeros((3, 3))
assert_aae(rsys.M[:3, :3], expected_mass)
assert_aae(rsys.M[3:, 3:], expected_inertia)
assert_aae(rsys.M[3:, :3], expected_offdiag)
assert_aae(rsys.M[:3, 3:], expected_offdiag.T)
