Cases of integrability corresponding to the pendulum motion on the plane

M. V. Shamolin

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 91-113

Résumé

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconservative force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

Détail

Keywords: rigid body, resisting medium, dynamical system, phase pattern, case of integrability.

Bibliographie

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