Jacobi equations using a variational principle

Details Jacobi equations using a variational principle Jacobi equations using a variational principle

2000-05-02

arxiv.org/abs/math-ph/0005005v2

Phys. Lett A v. 275 (2000) 218-222

Physics

Mathematical Physics

7 pages, no figures

Scientific paper

10.1016/S0375-9601(00)00574-0

A variational principle is proposed for obtaining the Jacobi equations in systems 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 the systems and can be related to the vertical extension of the Lagrangian formalism. To exemplify two of such aspects, we uncover a constant of motion in the Jacobi equations of autonomous systems and we recover the well-known sufficient conditions of stability of two dimensional orbits in classical mechanics.

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