A Random Player wrote:What I have so far is give the collection of objects an extra velocity to make the total translational momentum be 0. Then we calculate the "pulling" momentum of each mass by breaking the velocities into the radial and "towards/away from center" velocities. Add together the towards/away velocities. The remaining velocities are all radial. Calculate the total... Not sure what this is called. Distance of each object from CoM * mass * velocity. Find the average rotational momentum from those, then add up the velocity removed at the beginning and the sum of the towards/away velocities to get translational.

Is this right?

Ah, I see. Yeah, dealing with the velocities instead of the forces should be fine, then.

Looking over your steps -- that does look like a way to get the right answer. Though I'd probably take a very slightly different approach -- where you can skip the 'zero-ing' of the velocities at the beginning (and adding it back in at the end).

Step 1: Find linear momentum (and by extension, velocity): Add up the momentum of all the particles. Bam. Done.

This one's pretty darn easy, there. Since we know the total momentum of the system is the same whether you think of the pieces as connected or as separate, you can just straight up add the individual vectors. An easy, quick way to find the linear velocity of the rocket.

Step 2: Find the angular momentum: Basically what you said for this step. Break down each particle's velocity in to a radial portion (pointing toward the CoM or away from it) and a tangential portion (pointing at a right angle to the CoM). {as a heads up, I think you may have been misusing radial -- that's the one that heads in or out like, say, electric field lines.} Discard all the radial parts, since they don't contribute anything to spin. From the tangential part of the velocity, you can easily get the individual particle's angular momentum (as you said, distance to CoM*mass*tangential velocity). Add up those angular momenta, and you'll get the total angular momentum of the system.

Of course, you don't just care about the angular momentum... you'll want to know the speed with which it is spinning. And for that, you'll need to know the moment of inertia of the system. (Since, just as linear momentum = mass*linear velocity... angular momentum = moment of inertia*angular velocity) So, just calculate the moment of inertia at the same time as you figure out the CoM, I'd say.

Does this make sense?

Side note: I'll be excited to check out this project when you've got a build of it!