Jacobi equations using a variational principle

A variational principle is proposed for obtaining the Jacobi equations in s ystems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jacobi equations as well as in analysing the stability of solutions to the unperturbed system. To exemplify such aspects, we uncover a constant of motion in the Jacobi equations of any autonomous system, and we recover the sufficient conditions of stability of two dimensional orbits in classical mechanics. (C) 2000 Elsevier Science B.V. All rights reserved .