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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Analysis of Local Stability for Passive Walking Robot based on Spatial Operator Algebra Theory by Fei Lou, Wei Shen, Jing Guan, Guolin Ni

“…The result shows that, by using the theory of SOA, the Poincare-mapping function can be established effectively and fast, and avoids the complicated calculation of solving partial derivative in the modeling process by Lagrangian mechanics. At the same time, the analysis of local stability shows that passive walking robot must has stable fixed point for cycle stable walking, otherwise, it will occur period bifurcation.…”
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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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