def test_has_gyroscopic_forces_when_spinning(self):
# When the body is spinning, a torque should cause a
# perpendicular acceleration
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
A = 2.4 # perpendicular inertia
C = 5.7 # polar inertia
b = RigidBody('body', mass=7.04, inertia=diag([A, A, C]))
b.Rp[:, :] = rotmat_y(pi / 2)
b.vp[3:] = [spin, 0, precession]
update_skewmat(b.wps, b.vp[3:])
b.calc_mass()
# Expect moment of momentum to be [C*spin, 0, A*precession] in global
Jp = dot(b.Rp, dot(b.inertia, b.Rp.T))
hp = dot(Jp, b.vp[3:])
assert_array_almost_equal(hp, [C * spin, 0, A * precession])
# Expect the torque to be (precession * spin_speed) * (C - A)
# about the y axis
expected_Q2 = spin * precession * (C - A)
assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
def test_has_gyroscopic_forces_when_spinning(self):
# When the body is spinning, a torque should cause a
# perpendicular acceleration
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
A = 2.4 # perpendicular inertia
C = 5.7 # polar inertia
b = RigidBody("body", mass=7.04, inertia=diag([A, A, C]))
b.Rp[:, :] = rotmat_y(pi / 2)
b.vp[3:] = [spin, 0, precession]
update_skewmat(b.wps, b.vp[3:])
b.calc_mass()
# Expect moment of momentum to be [C*spin, 0, A*precession] in global
Jp = dot(b.Rp, dot(b.inertia, b.Rp.T))
hp = dot(Jp, b.vp[3:])
assert_array_almost_equal(hp, [C * spin, 0, A * precession])
# Expect the torque to be (precession * spin_speed) * (C - A)
# about the y axis
expected_Q2 = spin * precession * (C - A)
assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
def test_accounts_for_offset_centre_of_mass_in_mass_matrix(self):
# check mass matrix calculation when centre of mass is offset
# from proximal node.
b = RigidBody('body', mass=5.6, Xc=[1.2, 3.4, 5.4])
b.calc_mass()
# F = ma: a Z acceleration should produce a Z-force and X- and
# Y-moments.
F = -dot(b.mass_vv, [0, 0, 1, 0, 0, 0])
assert_array_equal(F, b.mass * array([0, 0, -1, -3.4, 1.2, 0]))
def test_accounts_for_offset_centre_of_mass_in_applied_force(self):
# check applied force due to gravity is correct
b = RigidBody("body", mass=5.6, Xc=[1.2, 3.4, 5.4])
s = System(gravity=9.81) # need a System to define gravity
s.add_leaf(b)
s.setup()
b.calc_mass()
b.calc_external_loading()
assert_array_equal(b.applied_forces, b.mass * 9.81 * array([0, 0, -1, -3.4, 1.2, 0]))
def test_accounts_for_offset_centre_of_mass_in_mass_matrix(self):
# check mass matrix calculation when centre of mass is offset
# from proximal node.
b = RigidBody("body", mass=5.6, Xc=[1.2, 3.4, 5.4])
b.calc_mass()
# F = ma: a Z acceleration should produce a Z-force and X- and
# Y-moments.
F = -dot(b.mass_vv, [0, 0, 1, 0, 0, 0])
assert_array_equal(F, b.mass * array([0, 0, -1, -3.4, 1.2, 0]))
def test_accounts_for_offset_centre_of_mass_in_applied_force(self):
# check applied force due to gravity is correct
b = RigidBody('body', mass=5.6, Xc=[1.2, 3.4, 5.4])
s = System(gravity=9.81) # need a System to define gravity
s.add_leaf(b)
s.setup()
b.calc_mass()
b.calc_external_loading()
assert_array_equal(b.applied_forces,
b.mass * 9.81 * array([0, 0, -1, -3.4, 1.2, 0]))
def test_calculates_mass_and_inertia_in_global_coordinates(self):
# simple rigid body at origin: this just checks the mass and
# inertia carry directly through to element mass matrix
II = diag([4.2, 6.7, 11.7])
b = RigidBody('body', mass=4.3, inertia=II)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_equal(b.mass_vv[3:, 3:], II)
assert_array_equal(b.quad_forces, 0)
# now rotate node by 90 deg about z axis, swapping x & y. This
# confirms that the mass part doesn't change, but the inertia
# matrix is updated.
b.Rp = rotmat_z(pi / 2)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_almost_equal(b.mass_vv[3:, 3:], diag([6.7, 4.2, 11.7]))
assert_array_equal(b.quad_forces, 0)
def test_calculates_mass_and_inertia_in_global_coordinates(self):
# simple rigid body at origin: this just checks the mass and
# inertia carry directly through to element mass matrix
II = diag([4.2, 6.7, 11.7])
b = RigidBody("body", mass=4.3, inertia=II)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_equal(b.mass_vv[3:, 3:], II)
assert_array_equal(b.quad_forces, 0)
# now rotate node by 90 deg about z axis, swapping x & y. This
# confirms that the mass part doesn't change, but the inertia
# matrix is updated.
b.Rp = rotmat_z(pi / 2)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_almost_equal(b.mass_vv[3:, 3:], diag([6.7, 4.2, 11.7]))
assert_array_equal(b.quad_forces, 0)
