Via compression ([18, 8]) we write the n-dimensional Chaplygin sphere system as an almost Hamiltonian system on T ∗SO(n) with internal symmetry group SO(n−1). We show how this symmetry group can be factored out, and pass to the fully reduced system on (a fiber bundle over) T S. This approach yields an explicit description of the reduced system in terms of… (More)

Via compression ([11, 7]) we write the n-dimensional Chaplygin sphere system as an almost Hamiltonian system on T SO(n) with internal symmetry group SO(n− 1). We show how this symmetry group can be factored out, and pass to the fully reduced system on (a fiber bundle over) T S. This approach yields an explicit description of the reduced system in terms of… (More)

The existence of an invariant measure for a system of differential equations is a very important property. From the point of view of dynamical systems, it is a key ingredient for the application of ergodic theory. It is also a crucial hypothesis in Jacobi’s theorem of the last multiplier that establishes integrability of the system via quadratures.… (More)