Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration

被引：1

作者：

Calleja, Renato ^{[1
]}

Doedel, Eusebius ^{[2
]}

Garcia-Azpeitia, Carlos ^{[3
]}

机构：

[1] Univ Nacl Autonoma Mexico, IIMAS, Matemat & Mecan, Admon 20, Mexico City 01000, DF, Mexico

[2] Concordia Univ, Dept Comp Sci, 1455 Blvd Maisonneuve O, Montreal, PQ H3G 1M8, Canada

[3] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City 04510, DF, Mexico

来源：

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS | 2016年 / 225卷 / 13-14期

关键词：

PERIODIC-ORBITS; INVARIANT-MANIFOLDS; RELATIVE EQUILIBRIA; LINEAR-STABILITY; SYSTEMS;

D O I：

10.1140/epjst/e2016-60009-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three equilibrium a"<currency> (n) -orbits from which families of Lyapunov orbits emerge. Numerical continuation of these families using a boundary value formulation is used to construct the bifurcation diagram for the case n = 7, also including some secondary and tertiary bifurcating families. We observe symmetry-breaking bifurcations in this system, as well as certain period-doubling bifurcations.

引用

页码：2741 / 2750

页数：10

共 14 条

[1]

[Anonymous], DIFFER EQU DYN SYST

[2] Restricted N+1-body problem: existence and stability of relative equilibria [J].

Bang, D ;

Elmabsout, B .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2004, 89 (04) :305-318

[3] Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem [J].

Calleja, R. C. ;

Doedel, E. J. ;

Humphries, A. R. ;

Lemus-Rodriguez, A. ;

Oldeman, E. B. .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2012, 114 (1-2) :77-106

[4]

DOEDEL EJ, 2003, INT J BIFURCAT CHAOS, V13, P1

[5] Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the n-body problem [J].

Garcia-Azpeitia, C. ;

Ize, J. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (05) :2033-2075

[6] Global bifurcation of planar and spatial periodic solutions in the restricted n-body problem [J].

Garcia-Azpeitia, C. ;

Ize, J. .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2011, 110 (03) :217-237

[7] The web of periodic orbits at L4 [J].

Henrard, J .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2002, 83 (1-4) :291-302

[8] Particle motions in Maxwell's ring dynamical systems [J].

Kalvouridis, Tilemahos J. .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2008, 102 (1-3) :191-206

[9] Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [J].

Koon, WS ;

Lo, MW ;

Marsden, JE ;

Ross, SD .

CHAOS, 2000, 10 (02) :427-469

[10] TRANSVERSALITY OF THE INVARIANT-MANIFOLDS ASSOCIATED TO THE LYAPUNOV FAMILY OF PERIODIC-ORBITS NEAR L2 IN THE RESTRICTED 3-BODY PROBLEM [J].

LLIBRE, J ;

MARTINEZ, R ;

SIMO, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1985, 58 (01) :104-156

← 1 2 →