Abstract
A Lagrangian form of dynamic equations for nonlinear nonholonomic constraints was studied by the first author in a previous paper. The aim of this paper is to put these equations in a cotangent form, according to some regularity conditions. It is particularized as an example to a decelerated motion of a free particle, when some dual simple equations are obtained.
Highlights
The geometrization of nonholonomic systems is a historically outstanding problem in mechanics and geometry
Nonlinear constraints are involved in nonholonomic mechanics; see, for example [20] and the citations therein
The result stated in Theorem 3.1 gives a synthetic form of linear and regular-nonlinear cases. This result can be adapted to other situations; for example, in the case of time dependent constraints, or of a time independent lagrangian
Summary
The geometrization of nonholonomic systems is a historically outstanding problem in mechanics and geometry (see, for example [14]). Bloch and we given a new form expressed in Theorem 3.1 Adapting these results in the case of time dependent nonlinear constraints, we obtain a similar general result that applies in the cases of generalized Chetaev case [16] or the examples therein. The result stated in Theorem 3.1 gives a synthetic form of linear and regular-nonlinear cases This result can be adapted to other situations; for example, in the case of time dependent constraints, or of a time independent lagrangian (as studied in [16] and the examples of the Appell-Hammel dynamic system in an elevator and the riemannian flow (see [20]). We notice that almost all formulas obtained, except for some explicit situations, have the same form in the simple (i.e. fibered manifold) case, as well as in the foliated case
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