Lax forms and the Euler top equations: A new approach

摘要

We consider the problem of torque-free spinning of a rigid body in the context of Lax representation from which the linearization of the nonlinear Euler top equations naturally arises. The Lax equation with Hermitian matrices leads to the two equivalent pictures of quantum mechanics, namely, the Schr?dinger and Heisenberg pictures. We derive a 3×3 Hamiltonian matrix based on principal moments of inertia and the Jacobi elliptic functions for the case of a 3-dimensional free rotation. We show generalization of our work for the n-dimensional case.