Quasiperiodic Forced Oscillations of a Solid Body in the Field of a Quadratic Potential

Abstract

We consider a natural Lagrangian system that describes the motion of a solid body under the action of superposition of two potential force fields. The first field is a stationary field with quadratic potential, while the potential of the second field is linear in the space and depends on time as a quasiperiodic function. We establish sufficient conditions under which this system has a classical hyperbolic quasiperiodic solution, which locally minimizes the Lagrangian averaged over time.