Geodesic
One family of conformally Hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 2, pp. 179-196

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We propose a method for constructing conformally Hamiltonian systems of dynamical equations whose invariant measure arises from the Hamiltonian equations of motion after a change of variables including a change of time. As an example, we consider the Chaplygin problem of the rolling ball and the Veselova system on the Lie algebra $e^*(3)$ and prove their complete equivalence.
Keywords: integrable system, nonholonomic system, Chaplygin ball, Veselova system. 
A. V. Tsiganov. One family of conformally Hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 2, pp. 179-196. http://geodesic.mathdoc.fr/item/TMF_2012_173_2_a0/
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