Perturbed pendulum-like motions of a rigid body about a fixed point

TL;DR

This paper investigates the complex behaviors of a heavy rigid body's pendulum-like motions under perturbations, introducing canonical variables and analyzing asymptotics near split separatrices to deepen understanding of its dynamics.

Contribution

It introduces canonical variables for simplified analysis and provides a detailed qualitative description of perturbed pendulum-like motions near split separatrices.

Findings

Analysis of homoclinic and heteroclinic orbits

Properties of perturbed motions in inertial space

Asymptotic behavior near split separatrices

Abstract

This paper is devoted to a detailed investigation of the perturbed pendulum-like motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are introduced. Characteristic properties of perturbed pendulum-like motions of the body in inertial space are studied. A qualitative description of asymptotics of pendulum-like motions in a neighbourhood of split separatrices is given.