def test_VelocityPoint():
x = Variable("x")
R0 = FrameReference()
R1 = FrameReference(R0, translation=(x, 0, 0))
point = Object(R1)
np.testing.assert_almost_equal(point.get(R1, "v"), (0, 0, 0))
np.testing.assert_array_equal(point.get(R0, "v"), (x.dt, 0, 0))
def test_BuildRotatedFrame_random():
R0 = FrameReference()
Ntests = 100
for i in range(Ntests):
angle = np.random.rand(1)
direction = getRandomUnit3DVector()
rotation = (angle, direction)
Ri = FrameReference(R0, rotation=rotation)
def test_RotationedPosition():
R0 = FrameReference()
R1 = FrameReference(R0, rotation=(np.pi / 2, (0, 0, 1)))
R2 = FrameReference(R1, translation=(1, 0, 0))
point = Object(R2)
np.testing.assert_almost_equal(point.get(R2, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point.get(R1, "p"), (1, 0, 0))
np.testing.assert_almost_equal(point.get(R0, "p"), (0, 1, 0))
def test_CompositionTranslation():
R0 = FrameReference()
R1 = FrameReference(R0, translation=(1, 0, 0))
R2 = FrameReference(R1, translation=(0, 1, 0))
R3 = FrameReference(R2, translation=(0, 0, 1))
point = Object(R3)
np.testing.assert_almost_equal(point.get(R3, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point.get(R2, "p"), (0, 0, 1))
np.testing.assert_almost_equal(point.get(R1, "p"), (0, 1, 1))
np.testing.assert_almost_equal(point.get(R0, "p"), (1, 1, 1))
def test_CompositionRotationsZ():
a, b, c = np.random.rand(3)
R0 = FrameReference()
R1 = FrameReference(R0, rotation=(np.pi / 2, "z"))
R2 = FrameReference(R1, rotation=(np.pi / 2, "z"))
R3 = FrameReference(R2, translation=(a, b, c))
point = Object(R3)
np.testing.assert_almost_equal(point.get(R3, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point.get(R2, "p"), (a, b, c))
np.testing.assert_almost_equal(point.get(R1, "p"), (-b, a, c))
np.testing.assert_almost_equal(point.get(R0, "p"), (-a, -b, c))
def test_TranslatedPosition():
R0 = FrameReference()
R1 = FrameReference(R0, translation=(1, 0, 0))
R2 = FrameReference(R0, translation=(0, 1, 0))
R3 = FrameReference(R0, translation=(0, 0, 1))
point1 = Object(R1)
point2 = Object(R2)
point3 = Object(R3)
np.testing.assert_almost_equal(point1.get(R1, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point1.get(R0, "p"), (1, 0, 0))
np.testing.assert_almost_equal(point2.get(R2, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point2.get(R0, "p"), (0, 1, 0))
np.testing.assert_almost_equal(point3.get(R3, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point3.get(R0, "p"), (0, 0, 1))
def test_KineticEnergy():
m = 1
x = Variable("x")
R0 = FrameReference()
R1 = FrameReference(R0, translation=(x, 0, 0))
point = Object(R1)
point.mass = m
v = point.get(R1, "v")
E = point.KineticEnergy(R1)
assert E == m * np.dot(v, v) / 2
v = point.get(R0, "v")
E = point.KineticEnergy(R0)
assert E == m * np.dot(v, v) / 2
def test_BuildTranslatedFrame_standard():
R0 = FrameReference()
R1 = FrameReference(R0, translation=(0, 0, 0))
R2 = FrameReference(R0, translation=(1, 0, 0))
R3 = FrameReference(R0, translation=(0, 1, 0))
R4 = FrameReference(R0, translation=(0, 0, 1))
R5 = FrameReference(R0, translation=(1, 0, 1))
R6 = FrameReference(R0, translation=(2, 1, 2))
R7 = FrameReference(R0, translation=(0, 1, 1))
def test_CompositionRotationsXYZ():
a, b, c = np.random.rand(3)
d, e, f = np.random.rand(3)
R0 = FrameReference()
R1 = FrameReference(R0, translation=(a, b, c))
R2 = FrameReference(R1, rotation=(np.pi / 2, "x"))
R3 = FrameReference(R2, rotation=(np.pi / 2, "y"))
R4 = FrameReference(R3, rotation=(np.pi / 2, "z"))
R5 = FrameReference(R4, translation=(d, e, f))
point = Object(R5)
np.testing.assert_almost_equal(point.get(R5, "p"), (0, 0, 0))
np.testing.assert_almost_equal(point.get(R4, "p"), (d, e, f))
np.testing.assert_almost_equal(point.get(R3, "p"), (-e, d, f))
np.testing.assert_almost_equal(point.get(R2, "p"), (f, d, e))
np.testing.assert_almost_equal(point.get(R1, "p"), (f, -e, d))
np.testing.assert_almost_equal(point.get(R0, "p"), (a + f, b - e, c + d))
def test_BuildInertialFrame():
R0 = FrameReference() # Inertial Frame of Reference
def test_BuildTranslatedFrame_random():
R0 = FrameReference()
Ntests = 100
for i in range(Ntests):
translation = np.random.rand(3)
Ri = FrameReference(R0, translation=translation)
def test_BuildRotatedFrame_standard():
R0 = FrameReference()
R1 = FrameReference(R0, rotation=(0, "x"))
R2 = FrameReference(R0, rotation=(0, "y"))
R3 = FrameReference(R0, rotation=(0, "z"))
R4 = FrameReference(R0, rotation=(np.pi / 2, "x"))
R5 = FrameReference(R0, rotation=(np.pi / 2, "y"))
R6 = FrameReference(R0, rotation=(np.pi / 2, "z"))
R7 = FrameReference(R0, rotation=(2 * np.pi, "x"))
R8 = FrameReference(R0, rotation=(2 * np.pi, "y"))
R9 = FrameReference(R0, rotation=(2 * np.pi, "z"))
R1 = FrameReference(R0, rotation=(0, (1, 0, 0)))
R2 = FrameReference(R0, rotation=(0, (0, 1, 0)))
R3 = FrameReference(R0, rotation=(0, (0, 0, 1)))
R4 = FrameReference(R0, rotation=(np.pi / 2, (1, 0, 0)))
R5 = FrameReference(R0, rotation=(np.pi / 2, (0, 1, 0)))
R6 = FrameReference(R0, rotation=(np.pi / 2, (0, 0, 1)))
R7 = FrameReference(R0, rotation=(2 * np.pi, (1, 0, 0)))
R8 = FrameReference(R0, rotation=(2 * np.pi, (0, 1, 0)))
R9 = FrameReference(R0, rotation=(2 * np.pi, (0, 0, 1)))
def test_SetInertia():
R0 = FrameReference()
bar = Object(R0)
bar.II = ((1, 0, 0), (0, 1, 0), (0, 0, 1))
def test_SetCenterMass():
R0 = FrameReference()
bar = Object(R0)
bar.CM = (1, 2, 3)
def test_SetMass():
R0 = FrameReference()
bar = Object(R0)
bar.mass = 3
def test_BuildWithName():
R0 = FrameReference()
bar = Object(R0, "bar")
plate = Object(R0, name="plate")
def test_BuildSecondFrame():
R0 = FrameReference()
R1 = FrameReference(R0)
def test_Build():
R0 = FrameReference()
bar = Object(R0)