Abstract
A method is proposed for computing nearly optimal trajectories of dynamic systems with a small parameter by splitting the original variational problem into two separate problems for "fast" and "slow" variables. The problem for "fast" variables is solved by improving the zeroth approximation — the extremals of the linearized problem — by the Ritz method. The solution of the problem for "slow" variables is constructed by passing from a discrete argument — the number of revolutions around the attracting center— to a continuous argument. The proposed method does not require numerical integration of systems of differential equations and produces a highly accurate approximate solution of the problem.
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Additional information
Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 113–118, 1989.
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Kiforenko, B.N., Goncharov, V.V. Quasiperiodic solutions of variational problems of motion in a central force field. J Math Sci 69, 1459–1462 (1994). https://doi.org/10.1007/BF01250592
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DOI: https://doi.org/10.1007/BF01250592