Jacobi fields of completely integrable Hamiltonian systems

TL;DR

This paper demonstrates that Jacobi fields in completely integrable Hamiltonian systems themselves form a completely integrable system, providing additional integrals that describe relative motion.

Contribution

It reveals that Jacobi fields form a completely integrable system, adding new integrals for understanding relative dynamics in such systems.

Findings

Jacobi fields constitute a completely integrable system

They provide m additional first integrals

These integrals characterize relative motion

Abstract

We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom also make up a completely integrable system. They provide m additional first integrals which characterize a relative motion.