Analysis and Control of Multi-body Dynamics by Nonlinear Discrete Integrable Theory

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For the purpose of classifying nonlinear discrete equations and their approximations in the series of fundamental equations appearing in multi-body dynamics, and presenting analyzable nonlinear discrete model, we have a obtained the following results.(1) We have studied a discrete model of an extensible string in three dimensional space and presented a new method of analyzing a string in space by the soliton theory. We have obtained some exact solutions by the soliton theory. The discrete basic equations are suitable for numerical simulations of string dynamics. Moreover, The model contains the bending and twisting, and becomes the special Cosserat elastic string art the continuous limit.(2) We have proposed a model to study the static strength of a quasi-isotropically reinforced random chopping glass/polypropylene composite. The model relates macroscopic and microscopic quantities, and is expected to be useful for the multi-body analysis.(3) We have studied discrete soliton equations which are reductions of the discrete model of multi-body dynamics and shown that the motion of a extensible string is well described by a soliton solution of two-component KP equation.(4) We have studied several discrete systems such as reaction-diffusion system and traffic flow, and shown that essential part of the phenomena are extracted by suitable discretizations.