Chaplygin ball in a solenoidal field

Abstract

According to Dirac, changes in the equations of motion related to additional external forces performing no work can be described in terms of deformations of the Poisson bracket. It is natural to ask whether or not Dirac’s ideas are valid in non-holonomic mechanics. We discuss this question here by taking the Chaplygin ball as an example. We consider the linear Lie–Poisson bracket on the Lie algebra e∗(3):