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International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 369-382
http://dx.doi.org/10.1155/S0161171280000257

Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators

Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284, Virginia, USA

Received 6 July 1979

Copyright © 1980 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We apply projection operator techniques to the computation of the natural frequencies of oscillation for three symmetrically coupled mechanical systems. In each case, the rotation subgroup of the full symmetry group is used to determine the projection operators with the result that the Lagrangian must be expressed in terms of complex-valued coordinates. In the coordinate system obtained from the action of the projection operators upon the original coordinates, the Lagrangian yields equations of motion which are separated to the maximum extent made possible by symmetry considerations.