Separation of variables in one partial integrable case of Goryachev

2010/12/20 by Pavel E. Ryabov, Ryabov, Pavel E.
Engineering · Mathematics · Physics and Astronomy · #70E17 #70G40 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1012.4379

openalex publication_date 2010/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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