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The problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian and give explicit forms corresponding to non-canonical Poissson brackets. Finally, we study the case where one of the gyrostats has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable in the zero order approximation.

Solid-liquid equilibrium of dipolar heteronuclear hard dumbbells in a generalized van der Waals theory: Application to methyl chloride Describing van der Waals Interaction in diatomic molecules with generalized gradient approximations: The role of the exchange functionalIn this paper we aim to prove that, except for the three known cases, the uniparametric family of Hamiltonian systems defined by the generalized van der Waals potential is nonintegrable in the Liouville-Arnold sense. The proof is based on the theorem of Morales and Ramis about nonintegrability by differential Galois theory.

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