Effective potential of a spinning heavy symmetric top when magnitudes of conserved angular momenta are not equal

TL;DR

This paper analyzes the effective potential of a spinning heavy symmetric top when the magnitudes of conserved angular momenta differ, revealing how the potential's minimum depends on their relative sizes and challenging existing separation assumptions.

Contribution

It provides a detailed analysis of the effective potential for a symmetric top with unequal conserved angular momenta, highlighting new behaviors and limitations of traditional separation methods.

Findings

Minimum of effective potential approaches a constant when one angular momentum exceeds the other.

Effective potential tends to infinity when the other angular momentum is greater.

Traditional strong or weak top separation methods are not universally applicable.

Abstract

There are various types of motion of a heavy symmetric top like regular precession, cusp like motion, rise of the top, etc. One of the tools used to understand that motion is effective potential. The effective potential for a spinning heavy symmetric top is studied when magnitudes of conserved angular momenta are not equal to each other. The dependence of effective potential on conserved angular momenta is analyzed. This study shows that the minimum of effective potential goes to a constant derived from conserved angular momenta when one of the conserved angular momenta is greater than the other one, and it goes to infinity when the other one is greater. It also shows that the usage of strong or weak top separation does not work adequately in all cases.