On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities
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We construct the Lagrange equation, Hamilton equation, and Birkhoff equation on the basis of given properties of motion under random perturbations. It is assumed that random perturbation forces belong to the class of Wiener processes and that given properties of motion are independent of velocities. The obtained results are illustrated by an example of motion of an Earth satellite under the action of gravitational and aerodynamic forces.
KeywordsInverse Problem Stochastic Differential Equation Wiener Process Aerodynamic Force Integral Curve
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- 3.I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Program Motion [in Russian], University of Friendship of Peoples, Moscow (1986).Google Scholar
- 4.V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems. Analysis and Filtration [in Russian], Nauka, Moscow (1990).Google Scholar
- 5.B. M. Tuladkhar, Construction of Equations of Lagrange, Hamilton, and Birkhoff Types on the Basis of Given Properties of Motion [in Russian], Abstract of the Doctoral-Degree Thesis (Physics and Mathematics), Moscow (1983).Google Scholar
- 6.M. I. Tleubergenov, Inverse Problems of Stochastic Differential Systems [in Russian], Abstract of the Doctoral-Degree Thesis (Physics and Mathematics), Alma-Ata (1999).Google Scholar
- 7.M. I. Tleubergenov and D. T. Azhymbaev, “On construction of a differential equation on the basis of given properties of motion under random perturbations,” Izv. Nats. Akad. Nauk Resp. Kazakh., Ser. Fiz.-Mat., No. 5, 15–20 (2007).Google Scholar
- 8.P. Sagirov, “Stochastic methods in dynamics of satellites,” Mekhanika, 147, No. 5, 28–47 (1974); 148, No. 6, 3–38 (1974).Google Scholar