Publicación: STABILITY, PERIODIC SOLUTION AND KAM TORI IN THE CIRCULAR RESTRICTED (N + 1)-BODY PROBLEM ON S3 AND H3
Fecha
2023
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JOURNAL OF NONLINEAR SCIENCE
Resumen
IN THIS ARTICLE, WE DEFINE A CIRCULAR RESTRICTED (N +1)-BODY PROBLEM ON THE SURFACES M3?,WITH ? = ±1. THE MOTION OF THE PRIMARIES CORRESPONDS TO AN ELLIPTIC RELATIVE EQUILIBRIA STUDIED IN DIACU (RELATIVE EQUILIBRIA OF THE CURVED N-BODY PROBLEM. ATLANTIS STUDIES IN DYNAMICAL SYSTEMS, ATLANTIS PRESS, PARIS, 2012), WHERE N IDENTICAL MASS PARTICLES ARE ROTATING UNIFORMLY AT THE VERTICES OF A REGULAR POLYGON PLACED AT A FIXED PARALLEL OF A MAXIMAL SPHERE. BY INTRODUCING ROTATING COORDINATES, THIS PROBLEM GIVES RISE TO A 3 D.O.F. HAMILTONIAN SYSTEM. THIS PROBLEM HAS AN EQUILIBRIUM POINT PLACED AT THE POLES OF S3 AND THE VERTEX OF H3, FOR ANY VALUE OF THE PARAMETERS. WE GIVE INFORMATION ABOUT THE LINEAR AND NONLINEAR STABILITY OF THESE EQUILIBRIA. FINALLY, WE CARRY OUT A STUDY ABOUT
THE EXISTENCE OF PERIODIC SOLUTIONS AND KAM TORI.
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Surfaces of constant curvature, Reduced Hamiltonian, Periodic solutions, Nonlinear stability, KAM tori, Hamiltonian formulation
