We discuss a Poisson structure, linear in momenta, for the generalized nonholonomic Chaplygin sphere problem and the $LR$ Veselova system. Reduction of these structures to the canonical form allows one to prove that the Veselova system is equivalent to the Chaplygin ball after transformations of coordinates and parameters.
Keywords:
nonholonomic mechanics, Poisson brackets
Citation:
Tsiganov A. V., On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems, Regular and Chaotic Dynamics,
2012, Volume 17, Number 5,
pp. 439-450