On non-linear periodic differential equations and associated point mappings. Application to stability problems

Bernussou, J.; Liu, H.; Mira, C.

doi:10.1016/0020-7462(76)90034-2

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1977

1989

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A study of nonlinear periodic systems via the point mapping method

Flashner¹,

Hsu²

1983

Numerical Meth Engineering

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SUMMARYIt 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 ~1 .~~ 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.

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