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We generalise Livens theorem, showing that Hamiltonian equation on the vectorbundle $E^\ast\rightarrow M$, dual to a general algebroid $E\rightarrow M$, canbe derived by means of a variational principle. The framework can be used todescribe Hamiltonian dynamics associated with (both vaconomic and nonholonomic)constraints in the bundle $E$.

Generalized Livens theorem and constrained Hamiltonian dynamics on algebroids