  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.
