Inertia around axis

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Hello folks!

I'm in a bit of a pickle trying to implement a stable spring-damper system for a physics game. Essentially, what I'm trying to do is to implement a semi stiff rotational relationship between two rigid bodies (I can't use joints for this). I came across an implementation I'd like to try at https://www.gamedev.net/tutorials/programming/math-and-physics/towards-a-simpler-stiffer-and-more-stable-spring-r3227/

but it requires the inertia for the objects in question. The problem is that I can't seem to find a way to get that value. I am aware that rigidbodies have a inertia tensor (not something I fully understand but I think I get the picture) but I can't seem to figure out how to use this to get the value that I need.

So in summary, I'm trying to figure out the inertia of any rigidbody around a given axis. Also I'd like to understand what happens if the axis does not go through the center of mass of the of the rigidbody.

Thanks for the help and sorry if I butchered the explanation :)

Answer 1

Answer by isaacdore1313 · May 26, 2020 at 04:11 PM

 public static float MomentOfInertiaAlongAxis(this Rigidbody rb, Vector3 axis) {
         axis = Quaternion.Inverse(rb.inertiaTensorRotation) * axis.normalized; //rotating the torque because it's equivalent and more efficient
         Vector3 angularAcceleration = new Vector3(Vector3.Dot(Vector3.right, axis) / rb.inertiaTensor.x, Vector3.Dot(Vector3.up, axis) / rb.inertiaTensor.y, Vector3.Dot(Vector3.forward, axis) / rb.inertiaTensor.z); //calculating the angular acceleration that would result from a torque of 1 Nm (the same way that unity does it)
         return 1 / angularAcceleration.magnitude; //moment of inertia = Torque / angular acceleration
     }

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manum_ · May 01 at 08:33 PM 0

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This works nicely for me. Could you explain a bit how it works? Or may I just use your code in a project that may become commercial at some point?

Inertia around axis

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