def test_combineInertiasAboutPoint_TShapedBlock(self):
# http://adaptivemap.ma.psu.edu/websites/A2_moment_intergrals/parallel_axis_theorem/pdf/ParallelAxis_WorkedProblem2.pdf
# T-shaped block
# Top block (1) dimensions are (4,2,0)
# Bottom block (2) dimensions are (2,4,0)
Ixx1 = 1 / 12 * 2 * 4**3
Ixx2 = 1 / 12 * 4 * 2**3
Iyy1 = Ixx2
Iyy2 = Ixx1
MOI1 = Vector(Ixx1, Iyy1, 0)
centroid1 = Vector(0, 3, 0)
mass1 = 8
inertia1 = Inertia(MOI1, centroid1, mass1, centroid1)
MOI2 = Vector(Ixx2, Iyy2, 0)
centroid2 = Vector(0, 0, 0)
mass2 = 8
inertia2 = Inertia(MOI2, centroid2, mass2, centroid2)
# Add them up at the overall centroid
overallCentroid = Vector(0, 1.5, 0)
combinedInertia = inertia1.combineInertiasAboutPoint([inertia2],
overallCentroid)
self.assertAlmostEqual(combinedInertia.MOI.X, 49.333333333333)
self.assertAlmostEqual(combinedInertia.mass, 16)
self.assertAlmostEqual(combinedInertia.CG, overallCentroid)
self.assertAlmostEqual(combinedInertia.MOICentroidLocation,
overallCentroid)
def test_InertiaAddition(self):
mCG1 = Inertia(Vector(0, 0, 0), Vector(0, 0, 2), 10)
mCG2 = Inertia(Vector(0, 0, 0), Vector(0, 0, 0), 20)
m3 = mCG1.combineInertiasAboutPoint([mCG2], Vector(0, 0, 0))
self.assertEqual(m3.mass, 30)
self.assertAlmostEqual(m3.CG.Z, 0.6666666666666)
def test_combineInertiasAboutPoint_SlenderRod(self):
# Test transforming from center to endpoint of slender rod
rodMOI = Vector(1 / 12, 1 / 12, 0)
rodCentroid = Vector(0, 0, 0)
rodMass = 1
rodCG = Vector(0, 0, 0)
centroidInertia = Inertia(rodMOI, rodCentroid, rodMass, rodCG)
rodEndPoint = Vector(0, 0, -0.5)
endPointInertia = centroidInertia.combineInertiasAboutPoint(
[], rodEndPoint)
assertIterablesAlmostEqual(self, endPointInertia.MOI,
Vector(1 / 3, 1 / 3, 0))
def test_combineInertiasAboutPoint_Dumbbell(self):
# http://adaptivemap.ma.psu.edu/websites/A2_moment_intergrals/parallel_axis_theorem/pdf/ParallelAxis_WorkedProblem3.pdf
# Two 40kg 0.2m diameter weights at each end
# One 20kg, 0.6m long bar between them
# (0,0,0) is at the center of the rod between the dumbbells
ballMOI = Vector(0.16, 0.16, 0.16)
ballCentroid1 = Vector(-0.4, 0, 0)
ballCentroid2 = Vector(0.4, 0, 0)
ballMass = 40
ball1Inertia = Inertia(ballMOI, ballCentroid1, ballMass, ballCentroid1)
ball2Inertia = Inertia(ballMOI, ballCentroid2, ballMass, ballCentroid2)
rodMOI = Vector(0, 0.6, 0.6)
rodCentroid = Vector(0, 0, 0)
rodMass = 20
rodInertia = Inertia(rodMOI, rodCentroid, rodMass, rodCentroid)
combinedInertia = ball1Inertia.combineInertiasAboutPoint(
[ball2Inertia, rodInertia], rodCentroid)
self.assertAlmostEqual(combinedInertia.MOI.Y, 13.72)
