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Lie algebroids and mechanics. (English) Zbl 0912.70009
The author considers the time-independent Lagrangian systems with non-holonomic constraints. A constrained mechanical system is understood as a triple \((M,L,C)\), where \(M\) is a manifold, \(L\) is a hyperregular Lagrangian on \(TM\), and \(C\subset TM\) is a constraint submanifold. The author gives a relation between the acceleration and the constraint force which generalizes Newton equation, examines the Hamiltonian point of view, derives constrained Hamilton equations and shows their equivalence to the constrained Lagrange equations. Finally the author investigates the Legendre transformation on Lie algebroids.

MSC:
70F25 Nonholonomic systems related to the dynamics of a system of particles
70H03 Lagrange’s equations
22E70 Applications of Lie groups to the sciences; explicit representations
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