This paper develops the theory of the reducing multiplier for a special class of nonholonomic dynamical systems, when the resulting nonlinear Poisson structure is reduced to the Lie–Poisson bracket of the algebra $e(3)$. As an illustration, the Chaplygin ball rolling problem and the Veselova system are considered. In addition, an integrable gyrostatic generalization of the Veselova system is obtained.
Keywords:
nonholonomic dynamical system, Poisson bracket, Poisson structure, reducing multiplier, Hamiltonization, conformally Hamiltonian system, Chaplygin ball
Citation:
Bolsinov A. V., Borisov A. V., Mamaev I. S., Geometrization of the Chaplygin reducing-multiplier theorem, Rus. J. Nonlin. Dyn.,
2013, Vol. 9, No. 4,
pp. 627-640
DOI:10.20537/nd1304002