Jacobi equations as Lagrange equations of the deformed Lagrangian

摘要

We study higher-order variational derivatives of a generic Lagrangian L(sub 0) = L(sub 0)(t,q,q). We introduce two new Lagrangians, L(sub 1) and L(sub 2), associated to the first and second-order deformations of the original Lagrangian L(sub 0). In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L(sub 1). We can furthermore introduce an associated Hamiltonian H(sub 1) = H(sub 1)(t,q,q radical,(eta),(eta) radical) with (eta) equivalent to (delta)q. If L(sub 0) is independent of time then H(sub 1) is a conserved quantity. (author). 15 refs. (Atomindex citation 26:048106)