def test_dof_index(self):
s = System()
j1 = FreeJoint('j1')
j2 = FreeJoint('j2')
s.add_leaf(j1)
j1.add_leaf(j2)
s.setup()
# Prescribe some of the strains:
# _____j1____ _____j2____
# Strain: 0 1 2 3 4 5 0 1 2 3 4 5
# Prescr: * * *
# Dofs: 0 1 2 3 4 5 6 7 8
s.prescribe(j1, 0, part=[1, 4])
s.prescribe(j2, 0, part=[3])
self.assertEqual(s.dof_index('j1', 0), 0)
self.assertEqual(s.dof_index('j1', 2), 1)
self.assertEqual(s.dof_index('j1', 5), 3)
self.assertEqual(s.dof_index('j2', 5), 8)
# Strain index out of range should give IndexError
with self.assertRaises(IndexError):
s.dof_index('j1', 6)
# Asking for index of prescribed strain should give ValueError
with self.assertRaises(ValueError):
s.dof_index('j1', 1)
def test_solve_accelerations(self):
# solve_accelerations() should find:
# (a) response of system to forces (here, gravity)
# (b) include any prescribed accelerations in qdd vector
g = 9.81
s = System(gravity=g)
j = FreeJoint('joint')
b = RigidBody('body', mass=23.54, inertia=52.1 * np.eye(3))
s.add_leaf(j)
j.add_leaf(b)
s.setup()
# Prescribe horizontal acceleration. Vertical acceleration
# should result from gravity.
s.prescribe(j, 2.3, part=[0]) # x acceleration
# Initially accelerations are zero
assert_aae(j.ap, 0)
assert_aae(j.ad, 0)
assert_aae(j.astrain, 0)
# Solve accelerations & check
s.solve_accelerations()
s.update_kinematics()
assert_aae(j.ap, 0) # ground
assert_aae(j.ad, [2.3, 0, -g, 0, 0, 0])
assert_aae(j.astrain, j.ad) # not always true, but works for FreeJoint
def test_solve_accelerations_coupling(self):
# Further to test above, check that coupling between prescribed
# accelerations and other dofs is correct. For example, if there
# is a rigid body vertically offset from the joint, then a
# prescribed horizontal acceleration should cause an angular
# acceleration as well as the translational acceleration.
s = System()
j = FreeJoint('joint')
c = RigidConnection('conn', [0, 0, 1.7])
b = RigidBody('body', mass=23.54, inertia=74.1 * np.eye(3))
s.add_leaf(j)
j.add_leaf(c)
c.add_leaf(b)
s.setup()
# Prescribe horizontal acceleration, solve other accelerations
s.prescribe(j, 2.3, part=[0]) # x acceleration
s.update_kinematics() # update system to show prescribed acc
s.solve_accelerations() # solve free accelerations
s.update_kinematics() # update system to show solution
# Ground shouldn't move
assert_aae(j.ap, 0)
# Need angular acceleration = (m a_x L) / I0
I0 = 74.1 + (23.54 * 1.7**2)
expected_angular_acc = -(23.54 * 2.3 * 1.7) / I0
assert_aae(j.ad, [2.3, 0, 0, 0, expected_angular_acc, 0])
assert_aae(j.astrain, j.ad) # not always true, but works for FreeJoint
def test_single_rigid_body(self):
mass = 36.2
inertia = np.diag([75.4, 653, 234])
s = System()
j = FreeJoint('joint')
b = RigidBody('body', mass, inertia)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
# Calculate reduced system to get rigid body matrices
rsys = ReducedSystem(s)
self.assertEqual(rsys.M.shape, (6, 6))
self.assertEqual(rsys.Q.shape, (6, ))
assert_aae(rsys.M[:3, :3], mass * np.eye(3))
assert_aae(rsys.M[3:, 3:], inertia)
assert_aae(rsys.M[3:, :3], 0)
assert_aae(rsys.M[:3, 3:], 0)
assert_aae(rsys.Q, 0)
# Now if some freedoms are prescribed, don't appear in reduced system
s.prescribe(j, part=[1, 2, 3, 4, 5]) # only x-translation is free now
rsys = ReducedSystem(s)
self.assertEqual(rsys.M.shape, (1, 1))
self.assertEqual(rsys.Q.shape, (1, ))
assert_aae(rsys.M[0, 0], mass)
assert_aae(rsys.Q, 0)
def test_single_rigid_body(self):
mass = 36.2
inertia = np.diag([75.4, 653, 234])
s = System()
j = FreeJoint('joint')
b = RigidBody('body', mass, inertia)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
# Calculate reduced system to get rigid body matrices
rsys = ReducedSystem(s)
self.assertEqual(rsys.M.shape, (6, 6))
self.assertEqual(rsys.Q.shape, (6,))
assert_aae(rsys.M[:3, :3], mass * np.eye(3))
assert_aae(rsys.M[3:, 3:], inertia)
assert_aae(rsys.M[3:, :3], 0)
assert_aae(rsys.M[:3, 3:], 0)
assert_aae(rsys.Q, 0)
# Now if some freedoms are prescribed, don't appear in reduced system
s.prescribe(j, part=[1, 2, 3, 4, 5]) # only x-translation is free now
rsys = ReducedSystem(s)
self.assertEqual(rsys.M.shape, (1, 1))
self.assertEqual(rsys.Q.shape, (1,))
assert_aae(rsys.M[0, 0], mass)
assert_aae(rsys.Q, 0)
def test_print_functions(self):
# Not very good tests, but at least check they run without errors
joint = FreeJoint('joint')
body = RigidBody('body', mass=1.235)
s = System()
s.add_leaf(joint)
joint.add_leaf(body)
s.setup()
s.print_states()
s.print_info()
def test_prescribe_free(self):
s = System()
j = FreeJoint('joint')
s.add_leaf(j)
s.setup()
s.time = 3.54
# Initially all 6 joint motions are free
self.assertEqual(len(s.q.dofs), 6)
# Prescribing joint to be fixed results in no dofs
s.prescribe(j)
self.assertEqual(len(s.q.dofs), 0)
# Freeing joint results in 6 dofs again
s.free(j)
self.assertEqual(len(s.q.dofs), 6)
# Prescribing 2 of joint motions leaves 4 dofs
s.prescribe(j, lambda t: t, [0, 2])
self.assertEqual(len(s.q.dofs), 4)
# Prescribing another joint motions leaves 3 dofs
s.prescribe(j, 2.0, part=3)
self.assertEqual(len(s.q.dofs), 3)
# Check accelerations are applied to qdd
assert_aae(s.qdd[j.istrain], 0)
s.apply_prescribed_accelerations()
assert_aae(s.qdd[j.istrain], [3.54, 0, 3.54, 2.0, 0, 0])
# Freeing joint results in 6 dofs again
s.free(j)
self.assertEqual(len(s.q.dofs), 6)
def test_dofs_subset(self):
s = System()
j = FreeJoint('joint')
s.add_leaf(j)
s.setup()
# 2 nodes, 6 constraints, 6 dofs
self.assertEqual(len(s.q), 2 * 12 + 6 + 6)
self.assertEqual(len(s.qd), 2 * 6 + 6 + 6)
self.assertEqual(len(s.qdd), 2 * 6 + 6 + 6)
self.assertEqual(len(s.q.dofs), 6)
self.assertEqual(len(s.qd.dofs), 6)
self.assertEqual(len(s.qdd.dofs), 6)
def test_get_set_state(self):
s = System()
j = FreeJoint('joint')
s.add_leaf(j)
s.setup()
# State is [q_dofs, qd_dofs].
# Here we have 6 dofs:
s.set_state([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
self.assertEqual(list(s.q.dofs), [1, 2, 3, 4, 5, 6])
self.assertEqual(list(s.qd.dofs), [7, 8, 9, 10, 11, 12])
s.q.dofs[2] = 100
s.qd.dofs[0] = -1
self.assertEqual(list(s.get_state()),
[1, 2, 100, 4, 5, 6, -1, 8, 9, 10, 11, 12])
