Abstract
We study strongly and weakly integrable 2-dimensional Hamiltonian systems with velocity dependent potentials. We determine the set of conditions which must be satisfied in order to allow the existence of an independent second invariant polynomial in the momenta. We then investigate the linear case for which a complete solution of the problem can be obtained. We recover the classical set of linear strongly integrable systems and provide several new examples of weakly integrable systems whose equations of motion can be explicitly solved at a fixed value of the energy.
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