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Numerical integration in Celestial Mechanics: a case for contact geometry

Abstract

Several dynamical systems of interest in Celestial Mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin–orbit model and the Lane–Emden equation all belong to such class. In this work, we start an investigation of these models from the point of view of contact geometry. In particular, we focus on the (contact) Hamiltonisation of these models and on the construction of the corresponding geometric integrators.

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Acknowledgements

The authors would like to thank the Bernoulli Institute for the hospitality. This research was partially supported by MS’s starter grant and NWO Visitor Travel Grant 040.11.698 that sponsored the visit of AB at the Bernoulli Institute. MS and FZ research is supported by the NWO project 613.009.10. MV is supported by the DFG through the SFB Transregio 109 “Discretization in Geometry and Dynamics”.

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Correspondence to Marcello Seri.

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Bravetti, A., Seri, M., Vermeeren, M. et al. Numerical integration in Celestial Mechanics: a case for contact geometry. Celest Mech Dyn Astr 132, 7 (2020). https://doi.org/10.1007/s10569-019-9946-9

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Keywords

  • Contact geometry
  • Geometric integrators
  • Modified Kepler
  • Spin–orbit
  • Lane–Emden

Mathematics Subject Classification

  • 65D30
  • 34K28
  • 34A26