Two dimentional lattice vibrations from direct product representations of symmetry groups by J. N. Boyd, P. N. Raychowdhury

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Representation theory of finite abelian groups applied to a linear diatomic crystal by J. N. Boyd, P. N. Raychowdhury

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The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator by Wang Guangbao, Ding Guangtao

“…The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. …”
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