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An introduction to mechanics with symmetry
M. de León, J. Cortés, D. Martín de Diego, S. Martínez
Recent Advances in Lie Theory, eds. I. Bajo, E. Sanmartin, Research and Exposition in Mathematics Series, vol. 25, Heldermann Verlag, 2002, pp. 305-332

Abstract

Symmetries are known to be an important instrument to reduce and integrate the equations of motion in Classical Mechanics through Noether theorems which provide conserved quantities. In this paper, some different types of infinitesimal symmetries are reviewed, from the almost classical results for unconstrained systems to the more recent research in nonholonomic mechanics. The case of vakonomic dynamics with some applications to optimal control theory is also discussed.

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