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1 Machine Dynamics Problems

1 1998

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Hamiltonian Systems on Linear Groups and One-Dimensional Lattices with Internal Parameters

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Sławianowski J. J. , Sławianowska A.

tom Vol. 20

263-273

Presented are some models of one-dimensional multiparticle systems with additional internal parameters responsible for the mutual binary interactions. The system consists of n point particles and n(n-1) repulsive and attractive "springs". The elastic coefficients of these springs are not constants but additional dynamical variables subject to certain law of motion on the same footing with lattice ppints. The model is strongly nonlinear but in principle, rigorously solvable. Mathematically, it is based on Hamiltonian systems on certain matrix groups. There are certain formal similarities to integrable chains well-known in the modern literature on nonlinear dynamics (Toda, 1981) like those studied by Calogero, Moser and Sutherland.