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Orbital Stability and Chaos with Incursive Algorithms for the Nonlinear Pendulum

Daniel M. Dubois

p. 3-20

    Abstract

    This paper deals with the Euler and Incursive algorithms of the nonlinear pendulum. The Euler algorithm is unstable. The incursive algorithms show a stable solution as an orbital stabilify for small values of the time step. For larger values of the time step, the incursive algorithms show an orbital stability for small values of the initial conditions and a chaotic sea for larger initial conditions.

    Index

    Keywords

    incursive algorithm, nonlinear pendulum, orbital stability, chaos

    Text

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    References

    Bibliographical reference

    Daniel M. Dubois, « Orbital Stability and Chaos with Incursive Algorithms for the Nonlinear Pendulum », CASYS, 14 | 2004, 3-20.

    Electronic reference

    Daniel M. Dubois, « Orbital Stability and Chaos with Incursive Algorithms for the Nonlinear Pendulum », CASYS [Online], 14 | 2004, Online since 20 August 2024, connection on 20 September 2024. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=2424

    Author

    Daniel M. Dubois

    asbl CHAOS, Centre for Hyperincursion and Anticipation in Ordered Systems, Institute of Mathematics B37, University of Liège, Grande Traverse, 12, B-4000 Liège 1, Belgium

    By this author

    Copyright

    CC BY-SA 4.0 Deed