Existence of a Center Manifold in a Practical Domain around L1 in the Restricted Three-Body Problem
نویسندگان
چکیده
We present a method of proving existence of center manifolds within specified domains. The method is based on a combination of topological tools, normal forms, and rigorous computer-assisted computations. We apply our method to obtain a proof of a center manifold in an explicit region around the equilibrium point L1 in the Earth–Sun planar restricted circular three-body problem.
منابع مشابه
Connecting Orbits and Invariant Manifolds in the Spatial Three-Body Problem
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold tubes associated to libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body ...
متن کاملConnecting orbits and invariant manifolds in the spatial restricted three-body problem
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-b...
متن کاملHeteroclinic Connections between Periodic Orbits and Resonance Tkansitions in Celestial Mechanics
This paper applies dynaanical system techniques to the problem of heteroclic connections and resonsnce transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis l)iswveny Mhsion. The main new technical...
متن کاملSPATIOTEMPORAL DYNAMIC OF TOXIN PRODUCING PHYTOPLANKTON (TPP)-ZOOPLANKTON INTERACTION
The present paper deals with a toxin producing phytoplankton (TPP)-zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. In the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. After that TPP-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both popu...
متن کاملDynamical Systems, the Three-Body Problem and Space Mission Design
This paper concerns heteroclinic connections and resonance transitions in the planar circular restricted 3-body problem, with applications to the dynamics of comets and asteroids and the design of space missions such as the Genesis Discovery Mission and low energy Earth to Moon transfers. The existence of a heteroclinic connection between pairs of equal energy periodic orbits around two of the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Applied Dynamical Systems
دوره 11 شماره
صفحات -
تاریخ انتشار 2012