Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem
- 68 Downloads
Intersections of families of three-dimensional periodic orbits which define bifurcation points are studied. The existence conditions for bifurcation points are discussed and an algorithm for the numerical continuation of such points is developed. Two sequences of bifurcation points are given concerning the family of periodic orbits which starts and terminates at the triangular equilibrium pointsL4,L5. On these sequences two trifurcation points are identified forµ = 0.124214 andµ = 0.399335. The caseµ = 0.5 is studied in particular and it is found that the space families originating at the equilibrium pointsL2,L3,L4,L5 terminate on the same planar orbitm1v of the familym.
KeywordsPeriodic Orbit Bifurcation Point Existence Condition Numerical Continuation Space Family
Unable to display preview. Download preview PDF.
- Contopoulos, G.: 1986,Celest. Mech. 38, 1.Google Scholar
- Goudas, C. L.: 1961,Bull. Soc. Math. Grece, Nouv. Ser. 2, 1.Google Scholar
- Goudas, C. L.: 1963,Icarus 2, 1.Google Scholar
- Hénon, M.: 1965,Ann. Astrophys. 28, 992.Google Scholar
- Hénon, M.: 1973,Astron. Astrophys. 28, 415.Google Scholar
- Perdios, E. and Markellos, V. V.: 1988,Celest. Mech. 42, 187.Google Scholar
- Whittaker, E.: 1904,A Treatise on the Analytical Dynamics, Cambridge University Press, Cambridge.Google Scholar
- Zagouras, C. G.: 1973, in B. Tapley and V. Szebehely (eds.),Recent Advances in Dynamical Astronomy, D. Reidel Publ. Co., Dordrecht, Holland, p. 156.Google Scholar
- Zagouras, C. G.: 1985,Celest. Mech. 37, 27 (Paper I).Google Scholar
- Zagouras, C. G. and Kazantzis, P. G.: 1979,Astrophys. Space Sci. 61, 389.Google Scholar
- Zagouras, C. G. and Markellos, V. V.: 1977,Astron. Astrophys. 59, 79.Google Scholar