Computing the inertia operator of a rigid body

Abstract

We prove that the inertia operator A of a rigid body is genetically determined, up to a scalar multiple, by the curve Ω in R3 that describes its angular velocity in the body. The precise condition is that Ω not be contained in a two-dimensional subspace of R3. We derive two indirect methods to compute A from the values of O over an arbitrary interval, and a direct method to compute A from the second-and fourth-order moments of Ω. The direct method utilizes moment identities derived from symmetries in Euler's equation. © 2001 American Institute of Physics.