A new 2D integrable system with a quartic second invariant

TL;DR

This paper introduces a novel 2D integrable system characterized by a quartic second invariant with 16 free parameters, extending classical rigid body dynamics cases and offering new insights into integrability.

Contribution

It presents a new integrable system with a quartic invariant involving multiple parameters, expanding the family of known integrable models in rigid body dynamics.

Findings

New integrable system with quartic invariant introduced

Special case relates to classical rigid body problems

System involves 16 free parameters

Abstract

In the present note we introduce a new solution of this equation, lead- ing to a new integrable system with a quartic integral, which involves 16 free parameters. A special case of the new system admits interpretation in a problem of rigid body dynamics. It gives a new integrable variation of the cases due to Kovalevskaya (1889), Chaplygin (1903) Goriatchev (1916) and Yehia (2006).