Comment on "The separation of variables and bifurcations of first integrals in one problem of D.N.Goryachev" by Pavel E. Ryabov (Archive:1102.2588v1)

TL;DR

This paper critiques Ryabov's application of the Kharlamov method to the Goryachev system, revealing it produces noncommutative separation variables rather than standard canonical ones.

Contribution

It clarifies the nature of the variables obtained via the geometric Kharlamov method in the Goryachev system, highlighting their noncommutative property.

Findings

The method yields noncommutative separation variables.

Standard canonical variables are not obtained by this approach.

The paper provides a clarification on the application of the Kharlamov method.

Abstract

We prove that in the Ryabov paper an application of the geometric Kharlamov method to the Goryachev system yields noncommutative "new variables of separation" instead of the standard canonical variables of separation.