Advanced Search
Article Contents
Article Contents

Symmetric periodic orbits in three sub-problems of the $N$-body problem

Abstract Related Papers Cited by
  • We study three sub-problems of the $N$-body problem that have two degrees of freedom, namely the $n-$pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of symmetric periodic orbits, including ``Schubart-like" orbits and brake orbits, by using topological shooting arguments.
    Mathematics Subject Classification: Primary: 70F07; Secondary: 37C27.


    \begin{equation} \\ \end{equation}
  • [1]

    R. Broucke, On the isosceles triangle configuration in the planar general three body problem, Astron. Astrophys., 73 (1979), 303-313.


    N. C. Chen, Periodic brake orbits in the planar isosceles three-body problem, Nonlinearity, 26 (2013), 2875-2898.doi: 10.1088/0951-7715/26/10/2875.


    J. Delgado and C. Vidal, The tetrahedral $4$-body problem, J. Dynam. Differential Equations, 11 (1999), 735-780.doi: 10.1023/A:1022667613764.


    D. Ferrario and A. Portaluri, On the dihedral $n$-body problem, Nonlinearity, 21 (2008), 1307-1321.doi: 10.1088/0951-7715/21/6/009.


    R. Martínez, On the existence of doubly symmetric "Schubart-like" periodic orbits, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 943-975.doi: 10.3934/dcdsb.2012.17.943.


    R. Martínez, Families of double symmetric ‘Schubart-like' periodic orbits, Celest. Mech. Dyn. Astr., 117 (2013), 217-243.doi: 10.1007/s10569-013-9509-4.


    R. McGehee, Triple collision in the collinear three-body problem, Invent. Math., 27 (1974), 191-227.doi: 10.1007/BF01390175.


    R. Moeckel, R. Montgomery and A. Venturelli, From brake to syzygy, Arch. Ration. Mech. Anal., 204 (2012), 1009-1060.doi: 10.1007/s00205-012-0502-y.


    R. Moeckel and C. Simó, Bifurcation of spatial central configurations from planar ones, SIAM J. Math. Anal., 26 (1995), 978-998.doi: 10.1137/S0036141093248414.


    R. Moeckel, A topological existence proof for the Schubart orbits in the collinear three-body problem, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 609-620.doi: 10.3934/dcdsb.2008.10.609.


    J. Schubart, Numerische Aufsuchung periodischer Lösungen im Dreikörperproblem, Astron. Nachr., 283 (1956), 17-22.doi: 10.1002/asna.19562830105.


    M. Shibayama, Minimizing periodic orbits with regularizable collisions in the $n$-body problem, Arch. Ration. Mech. Anal., 199 (2011), 821-841.doi: 10.1007/s00205-010-0334-6.


    C. Simó, Analysis of triple collision in the isosceles problem, in Classical Mechanics and Dynamical Systems, (eds. R L Devaney and Z H Nitecki ), New York: Marcel Dekker, (1981), 203-224.


    C. Simó and R. Martínez, Qualitative study of the planar isosceles three-body problem, Celest. Mech. Dyn. Astr., 41 (1987/88), 179-251. doi: 10.1007/BF01238762.


    A. Venturelli, A variational proof of the existence of von Schubart's orbit, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), 699-717.doi: 10.3934/dcdsb.2008.10.699.

  • 加载中

Article Metrics

HTML views() PDF downloads(139) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint