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Lagrangian system; constraints; nonholonomic constraints; constraint submanifold; canonical distribution; nonholonomic constraint structure; nonholonomic constrained system; reduced equations of motion (without Lagrange multipliers); Chetaev equations of motion (with Lagrange multipliers)
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 constraint submanifold) are presented. Finally, solvability of these equations is discussed and general solutions in explicit form are found.
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