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Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that(More)
We recall the Theorem by Lie and Scheffers concerning the characterization of systems of differential equations admitting a superposition function, i.e. those whose general solution can be written in terms of some particular solutions and constants. Each of these systems is related with a Lie algebra, specified by the own Theorem. We expose some recently(More)
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be related with equations on a Lie group and with some connections in fiber bundles. We develop two methods for dealing with(More)