Bounded Solutions to the System of 2-nd Order ODE and the Whitney pendulum

TL;DR

This paper establishes an existence theorem for bounded solutions to a system of second-order ordinary differential equations, with applications to dynamical systems such as the Whitney pendulum.

Contribution

It introduces a new existence theorem specifically for bounded solutions of second-order ODE systems, expanding the theoretical understanding of such systems.

Findings

Proved the existence of bounded solutions under certain conditions.

Applied the theorem to the Whitney pendulum model.

Enhanced understanding of the dynamics of second-order ODE systems.

Abstract

We propose the existence theorem for bounded solutions to the system of 2-nd order ODE. Dynamical applications have been considered.