Remarks on forced oscillations in some systems with gyroscopic forces

TL;DR

This paper investigates the existence of forced oscillations in two gyroscopic systems, demonstrating their occurrence under viscous friction in systems like a magnetic spherical pendulum and a rotating convex surface.

Contribution

It provides a proof of forced oscillations in gyroscopic systems with viscous friction, extending understanding of oscillatory behavior in such systems.

Findings

Forced oscillations exist in gyroscopic systems with viscous friction.

Existence proof applies to a magnetic spherical pendulum and a rotating convex surface.

Results enhance understanding of oscillations in gyroscopic systems with damping.

Abstract

In the paper we study the existence of a forced oscillation in two Lagrange systems with gyroscopic forces: a spherical pendulum in a magnetic field and a point on a rotating closed convex surface. We show how it is possible to prove the existence of forced oscillations in these systems provided the systems move in the presence of viscous friction.