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
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References
Verhulst, F., 1975, Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass, Celes. Mech. 11, 95–129
O'Malley, R.E., 1971, Boundary layer methods for nonlinear initial value problems, SIAM Rev. 13, 425–434
Verhulst, F., 1976, Matched asymptotic expansions in the two-body problem with quick loss of mass, J. Inst. Maths Applics 18, 87–98
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.
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
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