Inertia map as an index independent operation?

Projective GA
1

Hi all!
Trying to wrap my head around the inertia map in PGA, based on the description in the PGAdyn paper by Leo Dorst & Steven De Keninck. Is there a way to express the map in a more “GA operator” form without resorting to the index breakdown as used on page 27 (2.20) and (2.22) ?
It looks like it is some sort of scaling + dualisation in the body frame.

Thanks a bunch,
Mauritz

2

I am not sure about index independence especially when you transform inertia matrices of different objects from their body frames to the world frame to sum them up and then transform back to the body frame of the their composite object. But in eigenbasis you can do inertia mapping as diagonal matrix multiplication of the bivector B [e01, e02, e03, e12, e31, e23]

P=I[B]=\left(\begin{array}{cccccc} \text{i1} & 0 & 0 & 0 & 0 & 0 \\ 0 & \text{i2} & 0 & 0 & 0 & 0 \\ 0 & 0 & \text{i3} & 0 & 0 & 0 \\ 0 & 0 & 0 & m & 0 & 0 \\ 0 & 0 & 0 & 0 & m & 0 \\ 0 & 0 & 0 & 0 & 0 & m \\\end{array}\right)*Dual(B)
B=I^{-1}[P]=UnDual(\left(\begin{array}{cccccc} \text{i1} & 0 & 0 & 0 & 0 & 0 \\ 0 & \text{i2} & 0 & 0 & 0 & 0 \\ 0 & 0 & \text{i3} & 0 & 0 & 0 \\ 0 & 0 & 0 & m & 0 & 0 \\ 0 & 0 & 0 & 0 & m & 0 \\ 0 & 0 & 0 & 0 & 0 & m \\\end{array}\right)^{-1}*P)
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