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A study of nonlinear periodic systems via the point mapping method
Author(s) -
Flashner Henryk,
Hsu C. S.
Publication year - 1983
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620190204
Subject(s) - nonlinear system , dynamical systems theory , mathematics , ordinary differential equation , point (geometry) , polynomial , degree (music) , differential equation , mathematical analysis , computer science , algorithm , geometry , physics , quantum mechanics , acoustics
It is well known that one way to treat nonlinear periodic dynamical systems governed by ordinary differential equations is to find first the corresponding point mappings. This approach has many advantages but it has a main obstacle in that it is difficult to obtain the exact mapping except in very special cases. Presented in this paper is a procedure which allows us to determine the point mapping in a polynomial form up to any specific degree of accuracy. The procedure when applied to linear periodic systems reduces to the one proposed by Friedmann et al. 22 After presenting the algorithm for finding the point mappings, the method is applied to several problems in order to study the dynamical properties of the systems and to demonstrate the usefulness of the method.