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The description of jumps between Kepler orbits by boundary layer methods

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Part of the Lecture Notes in Mathematics book series (LNM,volume 711)

Abstract

The two-body problem with rapid loss of mass leads to the formulation of a singularly perturbed initial value problem. Asymptotic expansions are derived by the multiple time scales method when the mass decay is exponential. In other cases of mass decay this method breaks down and we use the method of matched asymptotic expansions or an integral equation method. Starting with the same initial orbits and ejecting the same amount of mass, the resulting orbits are different in the various cases of mass decay.

We prove the validity of the expansions on a long time-scale, [0,∞) or [0,1/ɛ), and we discuss possible extensions to more general initial value problems.

Keywords

  • Asymptotic Expansion
  • Integral Equation Method
  • Singular Perturbation Problem
  • Matched Asymptotic Expansion
  • Final Orbit

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Verhulst, F., 1975, Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass, Celes. Mech. 11, 95–129

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  2. O'Malley, R.E., 1971, Boundary layer methods for nonlinear initial value problems, SIAM Rev. 13, 425–434

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  3. Verhulst, F., 1976, Matched asymptotic expansions in the two-body problem with quick loss of mass, J. Inst. Maths Applics 18, 87–98

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  4. Verhulst, F., 1976, On the theory of averaging, in Long-time predictions in dynamics, 119–140, V. Szebehely and B. Tapley (eds.), D. Reidel Publ. Co., Dordrecht-Holland.

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  5. Hoppensteadt, F.C., 1966, Singular perturbations on the infinite interval, Trans.Am.Math.Soc. 123, 521–535.

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© 1979 Springer-Verlag

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Verhulst, F. (1979). The description of jumps between Kepler orbits by boundary layer methods. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062953

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  • DOI: https://doi.org/10.1007/BFb0062953

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09245-2

  • Online ISBN: 978-3-540-35332-4

  • eBook Packages: Springer Book Archive