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Variational integrators for orbital problems using frequency estimation

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Abstract

In this work, we present a new derivation of higher order variational integration methods that exploit the phase lag properties for numerical integrations of systems with oscillatory solutions. More specifically, for the derivation of these integrators, the action integral along any curve segment is defined using a discrete Lagrangian that depends on the endpoints of the segment and on a number of intermediate points of interpolation. High order integrators are then obtained by writing down the discrete Lagrangian at any time interval as a weighted sum of the Lagrangians corresponding to a set of the chosen intermediate points. The respective positions and velocities are interpolated using trigonometric functions. The methods derived this way depend on a frequency, which in general needs to be accurately estimated. The new methods, which improve the phase lag characteristics by re-estimating the frequency at every time step, are presented and tested on the general N-body problem as numerical examples.

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Authors and Affiliations

  1. Modelling and Simulation Centre, MACE, University of Manchester, Sackville Street, Manchester, UK

    Odysseas Kosmas

  2. Chair of Applied Dynamics, University of Erlangen-Nuremberg, Erlangen, 91058, Germany

    Sigrid Leyendecker

Authors
  1. Odysseas Kosmas
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  2. Sigrid Leyendecker
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Correspondence to Odysseas Kosmas.

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Communicated by: Tom Lyche

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Kosmas, O., Leyendecker, S. Variational integrators for orbital problems using frequency estimation. Adv Comput Math 45, 1–21 (2019). https://doi.org/10.1007/s10444-018-9603-y

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  • DOI: https://doi.org/10.1007/s10444-018-9603-y

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