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Orbit calculations near by the equilibrium points by a discrete mechanics method

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Abstract

Basic formulas of discrete mechanics in a rotating frame of references are obtained. Its application to several computer examples of orbits near by the equilibrium points of the Earth-Moon system are presented, and—for computational purposes—an algorithm is given.

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References

  • Bahvalov, N. S.: 1975,Čislennye Metody, Izdatel'stvo Nauka, Moscow.

    Google Scholar 

  • Brouwer, D. and Clemence, G.: 1961,Method of Celestial Mechanics, Academic Press.

  • Dubosin, J. W.: 1964,Nebesnaja Mehanika. Analitičeskie i kačestvennye metody, Izdatel'stvo Nauka, Moscow.

    Google Scholar 

  • Greenspan, D.: 1971,Introduction to Numerical Analysis and Applications, Markham, Chicago.

    Google Scholar 

  • Greenspan D.: 1972a, ‘New Forms of Discrete Mechanics’,Kybernetes 1, 87–101.

    Google Scholar 

  • Greenspan, D.: 1972b, ‘Discrete Newtonian Gravitation and then-Body Problem’,Utilitas Math. 2, 105–126.

    Google Scholar 

  • Greenspan, D.: 1973a, An Algebraic, Energy Conserving Formulation of Classical Molecular and Newtoniann-Body Interaction’,Bull. Am. Math. Soc. 2, 423–427.

    Google Scholar 

  • Greenspan, D.: 1973b, Symmetry in Discrete Mechanics,’Foundations of Physics 2, 247–253.

    Google Scholar 

  • Greenspan, D.: 1974, ‘Discrete Newtonian Gravitation and the Three-Body Problem,’Foundations of Physics 2, 299–310.

    Google Scholar 

  • Ralston, A.: 1971,Wstep do Analizy numeryczne J. PWN, Warsaw. In English: 1965,A First Course in Numerical Analysis, McGraw-Hill.

  • Sterne, T. E.: 1966,Wstep do Mechaniki nieba, PWN, Warsaw.

    Google Scholar 

  • Wierzbiński, S.: 1973,Mechanika nieba, PWN, Warsaw.

    Google Scholar 

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Albrycht, J., Marciniak, A. Orbit calculations near by the equilibrium points by a discrete mechanics method. Celestial Mechanics 24, 391–405 (1981). https://doi.org/10.1007/BF01230398

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  • DOI: https://doi.org/10.1007/BF01230398

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