On Integrable Perturbations of Some Nonholonomic Systems

TL;DR

This paper explores how classical methods for finding integrable potentials can be adapted to nonholonomic systems like Suslov, Veselova, and Chaplygin problems, revealing new integrable perturbations.

Contribution

It establishes a connection between Bertrand-Darboux equations in holonomic and nonholonomic systems, enabling the construction of integrable potentials for nonholonomic problems.

Findings

Derived nonholonomic integrable potentials from known holonomic potentials.

Extended classical Bertrand-Darboux methods to nonholonomic systems.

Identified relations between holonomic and nonholonomic integrability conditions.

Abstract

Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and Heisenberg problems are discussed in the framework of the classical Bertrand-Darboux method. We study the relations between the Bertrand-Darboux type equations, well studied in the holonomic case, with their nonholonomic counterparts and apply the results to the construction of nonholonomic integrable potentials from the known potentials in the holonomic case.