Celestial mechanics

, Volume 34, Issue 1–4, pp 357–368 | Cite as

The dynamics of bodies with variable masses

  • H. Lichtenegger


The Lie-series provide a convenient and simple method to solve systems of differential equations, especially in problems dealing with variable masses. A system of n-bodies moving isside a cloud and collecting mass is considered. The equations of motion are derived where-by the interchange of momentum is treated as a perturbation. It is shown that the solutions, represented by Lie-series, can be expressed by binomial expansions plus a perturbation which can be solved by interation. In addition, the motion of massless bodies experiencing frictional forces is briefly discussed.


Differential Equation Frictional Force Variable Mass Binomial Expansion Massless Body 
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  1. Gröbner, W.: 1967, Die Lie-Reihen und ihre Anwendungen VEB Deutscher Verlag der Wissenschaften, BerlinGoogle Scholar
  2. Gröbner, W., Knapp, H.: 1967a, Contribution to the Method of Lie-Series Bibliograph. Inst., MannheimGoogle Scholar
  3. Hanslmeier, A., Dvorak, R.: 1984, Numerical Integration with Lie-Series Astron. Astrophys.132, Nr. 1Google Scholar

Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • H. Lichtenegger
    • 1
  1. 1.Institut für AstronomieKarl-Franzens-UniversitätGrazAustria

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