Numerical studies to detect chaotic motion in the full planar averaged three-body problem

نویسندگان

چکیده

Abstract In this paper, the author deals with a well-known problem of Celestial Mechanics, namely three-body problem. A numerical analysis has been done in order to prove existence chaotic motions full-averaged particular configurations. Full because all three bodies have non-negligible masses and averaged Hamiltonian describing system respect fast angle. reduction degrees freedom phase-space is performed apply notion covering relations symbolic dynamics.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

15 صفحه اول

Stabilization of Chaotic Behavior in the Restricted Three-Body Problem

Henri Poincaré in his work on Celestial Mechanics underlined a possibility of chaotic behavior in threebody problem by the destruction of homoclinic contours. Later, an existence of transverse homoclinic points in the three-body problem was analytically verified. A well-known modification of the restricted three-body problem is that of Sitnikov [1960]. The Sitnikov problem takes place when two ...

متن کامل

Transition Tori in the Planar Restricted Elliptic Three Body Problem

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set of Lyapounov orbits survives the perturbation. The orbits are perturbed to quasi-periodic invariant tori. We show that for a certain family of m...

متن کامل

Symbolic Dynamics in the Planar Three-body Problem

1.1. Description of Results. Consider the motion of three point masses, m1, m2, m3, in a plane under the influence of their mutual gravitational attraction. This motion can be described by a Hamiltonian dynamical system of three degrees of freedom. In this paper, symbolic dynamical methods will be used to prove the existence of solutions of this Hamiltonian system which exhibit certain interest...

متن کامل

A trial symbolic dynamics of the planar three - body problem

Symbolic dynamics is applied to the planar three-body problem. Symbols are defined on the planar orbit when it experiences a syzygy crossing. If the body i is in the middle at the syzygy crossing and the vectorial area of the triangle made with three bodies changes sign from + to −, number i is given to this event, whereas if the vectorial area changes sign from − to +, number i+3 is given. We ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bollettino Dell'unione Matematica Italiana

سال: 2023

ISSN: ['2198-2759', '1972-6724']

DOI: https://doi.org/10.1007/s40574-023-00360-0