# On Periodic Solutions to Lagrangian System With Singularities

## TL;DR

This paper investigates periodic solutions in a Lagrangian system with singularities, where the configuration space varies over time, providing new insights into such complex dynamical systems.

## Contribution

It introduces a method to find periodic solutions in Lagrangian systems with time-dependent non-compact configuration spaces and singularities.

## Key findings

- Existence of a set of periodic solutions identified.
- Method applicable to systems with time-dependent configuration spaces.
- Advances understanding of dynamics with singularities.

## Abstract

A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.