# Hamiltonization and separation of variables for Chaplygin ball on a rotating plane

## TL;DR

This paper explores the Hamiltonization and separation of variables for the Chaplygin ball on a rotating plane, revealing new integrable structures and explicit variables of separation in specific cases.

## Contribution

It introduces a non-Hamiltonian vector field for the Chaplygin ball on a rotating plane and expresses it via Hamiltonian vector fields using a non-algebraic deformation of Poisson structures.

## Key findings

- Expressed the vector field via Hamiltonian structures in special cases
- Calculated variables of separation for the symmetric ball
- Constructed compatible Poisson brackets and Lax matrices

## Abstract

We discuss a non-Hamiltonian vector field appearing in consideration of a partial motion of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In two partial cases this vector field is expressed via Hamiltonian vector fields using a non-algebraic deformation of the canonical Poisson bivector on e^*(3). For the symmetric ball we also calculate variables of separation, compatible Poisson brackets, algebra of Haantjes operators and 2x2 Lax matrices.