Ukrainian Mathematical Journal

, Volume 62, Issue 7, pp 1163–1173 | Cite as

On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities

  • M. I. Tleubergenov
  • D. T. Azhymbaev

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.


Inverse Problem Stochastic Differential Equation Wiener Process Aerodynamic Force Integral Curve 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • M. I. Tleubergenov
    • 1
  • D. T. Azhymbaev
    • 1
  1. 1.Institute of Mathematics, Ministry of Education and Science of Kazakhstan RepublicAlma-AtaKazakhstan

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