Application of Computer Algebra for Construction of Quasi-periodic Solutions for Restricted Circular Planar Three Body Problem

  • V. P. Borunov
  • Yu. A. Ryabov
  • O. V. Surkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4194)


The algorithm is realized (with the help of computer algebra methods) for construction of numeric-analytical quasi-periodic solutions of precise(!) equations of restricted planar circular three-body problem (Sun–Jupiter-small planet) for an arbitrary sufficiently wide variety of initial data. This algorithm and corresponding exe-code allows us to obtain solutions in automatic mode (certainly, approximate but satisfying the motion equations with user-specified high precision) represented by twofold Fourier polynomials. Besides, the development of so-called perturbation function is not required (essential fact). These solutions are valid in principle for infinite time interval unlike known classical solutions of such problem. Such solutions are obtained for the first time.


Computer Algebra Quadratic Convergence Sequential Approximation Simple Iteration Minor Planet 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • V. P. Borunov
    • 1
  • Yu. A. Ryabov
    • 2
  • O. V. Surkov
    • 2
  1. 1.Computing Center of RASMoscow
  2. 2.Moscow Auto and Highway Construction Inst. (Technical University) 

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