Quasi-Chaplygin systems and nonholonimic rigid body dynamics

Abstract

We show that the Suslov nonholonomic rigid body problem studied in by Fedorov and Kozlov (Am. Math. Soc. Transl. Ser. 2 168:141-171, 1995), Jovanovic (Reg. Chaot. Dyn. 8(1):125-132, 2005), and Zenkov and Bloch (J. Geom. Phys. 34 (2):121-136, 2000) can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori.