General solution and invariants for a class of Lagrangian equations governed by a velocity-dependent potential energy

Publisher Website
Google Scholar
Abstract
It is shown that every generalized force derived from a velocity- dependent potential energy and independent of the acceleration, can be written as an n dimensional 'Lorentz force' with quantities E and B satisfying generalized Maxwell equations. The equations of motion in an n dimensional cartesian space and with B=B(T)B0 are integrated after reduction to canonical form. Expressions for two sets of invariants of the system are constructed and a relationship is shown with a class of well known exact and adiabatic invariants for the motion of a time-dependent harmonic oscillator and of a charged particle in a uniform time-dependent magnetic field.