Matrix of inertia with respect to a reference frame

[sogartar]

I know I can get the matrix of inertia with respect to the global coordinate system with

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App.ActiveDocument.getObjectsByLabel("myobject")[0].Shape.MatrixOfInertia

I have a local coordinate system. How can I get the matrix of inertia with respect to that coordinate system?

[edwilliams16]

The "global" MOI is the moment of inertia of the object about its CG with coordinate axes aligned with the global system. If what you want is the MOI about its CG with respect to the local coordinate axes, this will do it:

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obj = App.ActiveDocument.getObjectsByLabel("myobject")[0]
globalRotMatrix = obj.getGlobalPlacement().Rotation.toMatrix()
globalmoiObj = obj.Shape.MatrixOfInertia
localmoiObj =  globalRotMatrix.transposed() * globalmoiObj * globalRotMatrix

If you actually wanted the MOI with respect to the coordinate origin, we'll need to add the parallel axes theorem contribution of the moment of the CG about the origin.

EDIT to include that contribution:

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def outerProduct(v1,v2):
    '''return outer product of two Vectors  v1_i*v2_j (4 x 4) Matrix'''
    m = App.Matrix(v1.x*v2.x, v1.x*v2.y, v1.x*v2.z, 0, v1.y*v2.x, v1.y*v2.y, v1.y*v2.z ,0, v1.z*v2.x, v1.z*v2.y, v1.z*v2.z,0, 0, 0, 0, 0)
    return m

obj = App.ActiveDocument.getObjectsByLabel("myobject")[0]
globalRotMatrix = obj.getGlobalPlacement().Rotation.toMatrix()
globalmoiObj = obj.Shape.MatrixOfInertia
localmoiObj =  globalRotMatrix.transposed() * globalmoiObj * globalRotMatrix
v = obj.Placement.Base
mass = obj.Shape.Mass
localFromOriginmoiObj = localmoiObj + outerProduct(mass * v, v)

App.Matrix could use a multiply by scalar method.