Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators. (1980)

• Record Type: Journal Article
• Authors: Boyd, J. N.; Raychowdhury, P. N.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 3:Number 2(1980)
• Page Start: 369
• Page End: 382
• Publication Date: 1980
• Subjects: group representations -- harmonic oscillators -- Lagrangian mechanics -- natural frequencies -- projection operators; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171280000257
• Languages: English
• ISSNs: 0161-1712

Abstract

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.