The Three Body Problem

日期 : Jan 2016 - Jun 2016

This project was basically related to field of Astronomy,example of three body problem is motion of Earth,Moon and Sun and also form differential equation of three body problem.Abstract of that project is The Three Body problem is a special case of n-body Problem.The Three Body Problem describes the motion of three gravitating bodies under each other's gravitating influence.It is one of the oldest problems in Classical Mechanics,and has attracted attention of many scientist for more than 300 hundred years,they attempted to model the dynamics of celestial bodies in space.But they conclude that the only model which has been completely solved is that of The two body problem.Thus Three body problem is an good example for our introduction to Classical Mechanics.In this project, Lagrangian and Hamilton's Mechanics will be discussed and the main objective of this project is to a give mathematical description of three body problem. The three body problem is special case of n body problem.In the three-body problem, three bodies move in space under their mutual gravitational interaction as described by newtons theory of gravity.The most simple and typical sample of the three body problem is the motion of the sun,earth and moon in the solar system.Modeling three bodies may seem simple at first but,the fact is that ,it is a quite duanting task.Many methods have been used to solve this problem but no exact solution exist. The dynamic of three body is totally different from two body problem.In general, motion of three bodies take place in three dimension( 3D) and there is no restriction on their masses and initial condition.At first glance, the difficulty of the problem is not obvious,especially when considering that the two body problem has well known solution in closed form in terms of elementary function.Adding one extra body makes the problem too much complicated to obtain similar types of solutions.