Motion of the heavy symmetric top when magnitudes of conserved angular momenta are different

TL;DR

This paper classifies the motion types of a symmetric top using constants of motion, analyzing how different initial conditions affect the dynamics and providing numerical solutions for various motion scenarios.

Contribution

It introduces a method to classify symmetric top motions based on conserved angular momenta and explores the effects of initial conditions on the dynamics.

Findings

Classification of motion types using constants of motion

Numerical solutions illustrating different motion scenarios

Insights into how initial conditions influence precession and spin directions

Abstract

A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the beginning, but the top's overall precession can be positive; or initially, the gyroscope spins in one direction, but in a later stage one can find it while spinning in the other direction. On the other hand, if one knows different properties and types of motion, one can know what will happen. In this work, we have studied the classification of motion type by using constants of motion. We have also studied changes in dynamic variables. We have given examples of different types of motion and solved them numerically.