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_gyroscopic_acceleration(self):
"""When the body is spinning, a torque should cause a perpendicular
acceleration"""
from nose import SkipTest
raise SkipTest
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
length = 3.5
radius = 1.2
mass = 6.54
# Calculate inertias
A = mass * (3 * radius**2 +
2 * length**2) / 12 # perpendicular inertia
C = mass * radius**2 / 2 # polar inertia
# Make a uniform beam representing a gyroscope spinning around
# the beam's axis
b = UniformBeam('beam',
length=length,
density=mass / length,
Jx=C,
EA=1,
EIy=1,
EIz=1) # these don't matter
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(diag([C, A, A]), 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)
Q2_at_centre = b.quad_forces[4] + b.quad_forces[10] + \
(length/2)*(b.quad_forces[2] - b.quad_forces[8])
#assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
assert_array_almost_equal(Q2_at_centre, expected_Q2)
def test_gyroscopic_acceleration(self):
"""When the body is spinning, a torque should cause a perpendicular
acceleration"""
from nose import SkipTest
raise SkipTest
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
length = 3.5
radius = 1.2
mass = 6.54
# Calculate inertias
A = mass * (3*radius**2 + 2*length**2) / 12 # perpendicular inertia
C = mass * radius**2 / 2 # polar inertia
# Make a uniform beam representing a gyroscope spinning around
# the beam's axis
b = UniformBeam('beam', length=length, density=mass/length, Jx=C,
EA=1, EIy=1, EIz=1) # these don't matter
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(diag([C, A, A]), 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)
Q2_at_centre = b.quad_forces[4] + b.quad_forces[10] + \
(length/2)*(b.quad_forces[2] - b.quad_forces[8])
#assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
assert_array_almost_equal(Q2_at_centre, expected_Q2)
def test_update_skew(self):
x = zeros((3, 3))
for v in ([0, 0, 0], [1, 2, 3]):
update_skewmat(x, v)
assert_array_equal(x, skewmat(v))
def test_update_skew(self):
x = zeros((3, 3))
for v in ([0, 0, 0], [1, 2, 3]):
update_skewmat(x, v)
assert_array_equal(x, skewmat(v))