\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A Variational proof of the existence of Von Schubart's orbit

Abstract Related Papers Cited by
  • Weconsiderthecollinearthree-bodyproblemwithtwoequalmasses for the Newtonian potential $1/r$. We give a rigorous proof of the existence of a symmetric periodic solution with two collisions per period. This solution has been discovered numerically in 1956 by J. von Schubart (see [12]). Our proof is based on the direct method in Calculus of Variations, which consists in the minimization of the action on a well chosen set of periodic loops. The main difficulty is to show that the minimizer has only two collisions per period.
    Mathematics Subject Classification: Primary: 70F07, 70F15; Secondary: 37J50.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(105) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return