Separation of variables in one partial integrable case of Goryachev

TL;DR

This paper demonstrates that in a specific partial integrable case of Goryachev's rigid body dynamics, the equations of motion can be separated using hyperelliptic functions, with explicit algebraic expressions for phase variables.

Contribution

It introduces a method to separate variables in a partial integrable case of Goryachev's equations using hyperelliptic functions and explicit algebraic formulas.

Findings

Equations are separable via hyperelliptic functions.

Phase variables are expressed explicitly in algebraic functions.

Provides a new approach to solving this integrable case.

Abstract

We show that the equations of motion in one partial integrable case of Goryachev in the rigid body dynamics can be separated by the appropriate change of variables, the new variables x, y being hyperelliptic functions of time. The natural phase variables (components of coordinates and momenta) are expressed via x,y explicitly in elementary algebraic functions.