(all of this is in 2D)
I have two rigid bodies B1 and B2 that are fixed wrt each other -- in effect forming a single rigid body B which is the "union" of B1 and B2.
The mass of B is just the sum of the masses of B1 and B2, and the position of the center-of-mass of B is (I'm pretty sure) just the sum of the c-o-m positions of B1 and B2 weighted by their relative masses.
Is there a "simple" method to calculate the moment of inertia of B (around B's c-o-m) using the mass and moment of inertia of B1 and B2?
Obviously I could use whatever method I used to calculate B1 and B2's moments of inertia -- assuming that I'm using a general area-integration or point-sampling method, and not just sticking to simple primitives whose moments can be calculated with a simple formula.
However, I have a feeling that i should be able to use the mass and moments of B1 and B2 to make things much simpler.
In trying to find a solution to this problem, I've come across this article by Jonathan Blow which presents the concept of a "covariance body":
http://number-none.com/product/My%20Fri ... index.html
Calculating the covariance matrix seems similar to calculating the moment of inertia using point-samples, and handily enough in the "Manipulation" section near the bottom, he shows how you can easily combine covariance bodies.
However, I'm not sure that I'm understanding this correctly since the covariance matrix is a full 2x2 matrix, while the moment of inertia is a scalar.. or possibly diagonal matrix, I haven't touched physics stuff in a few months
Either way, it doesn't seem like the two are identical, only similar.. and I'd prefer to use moments calculated "properly" than to rely on point-sampling.I've also discovered that the "Composite Rigid Body Method" is a robotics/articulated-body method based on just what I want to do: consider two rigid bodies to be a single rigid body.
However, I haven't found a paper that's sufficiently introductory for me to understand given my fairly weak background in math (basic linear algebra).. every paper seems obsessed with "spatial algebra"/reduced coordinates, which I find a bit confusing.
Anyway.. if there is indeed a simple solution I'd love to know.
EDIT: of course, after a half-day of looking for a solution, 30 seconds after posting I came across the solution: the parallel axis theorem, which lets me calculate the moment of inertia of each of B1 and B2 relative to B's c-o-m. I'm going to leave this post up anyway in the hopes that someone else finds this useful.