Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type

Abstract

We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system.

References in corpus (2)

• Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
• Helmholtz conditions and symmetries for the time dependent case of the inverse problem of the calculus of variations