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A geometrical framework for the study of non-holonomic Lagrangian systems. (English) Zbl 0858.70013
The purpose is to describe some geometrical aspects of dynamical systems which are modelled by a system of second order differential equations, coupled with first order equations linear in derivatives. The corresponding constraints have a natural interpretation in terms of the Ehresmann connection on an appropriate bundle. The concepts of symmetry and adjoint symmetry are discussed for such systems; to this end, the authors introduce the notions of “dynamical covariant derivative” and “Jacobi endomorphism”.
The vertically rolling disc is chosen as an example to illustrate the proposed formalism and results.

MSC:
70H03 Lagrange’s equations
70F25 Nonholonomic systems related to the dynamics of a system of particles
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