Variational integrators for forced Birkhoffian systems

In this letter, we first extend the Pfaff–Birkhoff principle to include forces and obtain the Pfaff–Birkhoff–D’Alembert principle consequently. Well then motions of forced Birkhoffian systems coincide with extremals of the modified principle. Subsequently, compared with the continuous case, the disc...

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Bibliographic Details
Published in:Applied mathematics and computation 2013-12, Vol.225, p.326-332
Main Authors: Kong, Xinlei, Wu, Huibin, Mei, Fengxiang
Format: Article
Language:English
Subjects:
Algorithms
Computation
Construction
Discrete forced Birkhoffian equations
Integrators
Mathematical analysis
Mathematical models
Pfaff–Birkhoff–D’Alembert principle
Variational integrator
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Summary:In this letter, we first extend the Pfaff–Birkhoff principle to include forces and obtain the Pfaff–Birkhoff–D’Alembert principle consequently. Well then motions of forced Birkhoffian systems coincide with extremals of the modified principle. Subsequently, compared with the continuous case, the discrete forced Birkhoffian equations are constructed by discretizing the Pfaff–Birkhoff–D’Alembert principle. Considered as algorithms, the discrete equations have good numerical behavior in terms of getting the correct amounts by which the energy changes over the integration process, demonstrated by the given example.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.09.045