Abstract
A program to integrate the equations of motion by series in powers of the time step can be easily modified to furnish the elements of the matrizant in power series of the time step. In particular, if the series representing the motion are obtained recursively, differentiation of the recurrence relations will provide immediately a recursive scheme for computing the coefficient in the power series for the elements of the matrizant.
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References
Deprit, A. and Price, J.: 1965, ‘The Computation of Characteristic Exponents in the Planer Restricted Problem of Three Bodies’, Boeing Scientific Research Lab. Math. Note No. 415.
Goodyear, W.: 1965,Astron. J. 70, 189.
Hartwell, G.: 1968, ‘A Power Series Solution for the Motion of an Artificial Satellite and its Concomitant Variational Equations’, presented at 7th Astrodynamics Conference, Goddard Space Flight Center, April 1968.
Schanzle, A.: 1968,Power Series Representation of Partial Derivatives Required in Orbit Determination, Final Technical Report for NASA Goddard Space Flight Center Contract NAS 5-9756-59.
Steffensen, J. R.: 1956,Kg. Danske Videnskab, Selskab, Mat-Fys. Medd. 30, No. 18.
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Schanzle, A.F. Power series representation of partial derivatives required in orbit determination. Celestial Mechanics 4, 287–294 (1971). https://doi.org/10.1007/BF01231391
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DOI: https://doi.org/10.1007/BF01231391