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Several examples of nonholonomic mechanical systems

Martin Swaczyna (2011)

Communications in Mathematics

A unified geometric approach to nonholonomic constrained mechanical systems is applied to several concrete problems from the classical mechanics of particles and rigid bodies. In every of these examples the given constraint conditions are analysed, a corresponding constraint submanifold in the phase space is considered, the corresponding constrained mechanical system is modelled on the constraint submanifold, the reduced equations of motion of this system (i.e. equations of motion defined on the...

Sui moti polinomiali

Franco De Franchis (1970)

Rendiconti del Seminario Matematico della Università di Padova

Sur la description intrinsèque des grandeurs dimensionnelles

J.-C. Houard (1981)

Annales de l'I.H.P. Physique théorique

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...

Systèmes hamiltoniens k-symplectiques.

Azzouz Awane, Mohamed Belam, Sadik Fikri, Mohammed Lahmouz, Bouchra Naanani (2002)

Revista Matemática Complutense

We study some properties of the k-symplectic Hamiltonian systems in analogy with the well-known classical Hamiltonian systems. The integrability of k-symplectic Hamiltonian systems and the relationships with the Nambu's statistical mechanics are given.