Numerical experience with the three-body problem

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.

Three - Body Problem

A Trilinear Three-Body Problem

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...

Numerical Computation of Normal Forms around some Periodic Orbits of the Restricted Three Body Problem

In this paper we introduce a general methodology for computing numerically the normal form around a periodic orbit of an autonomous analytic Hamiltonian system The process follows two steps First we expand the Hamiltonian in suit able coordinates around the orbit and second we perform a standard normal form scheme based on the Lie series method This scheme is carried out up to some nite order a...

Contemporary Status of the Three-Body Problem with Coulomb Interactions