Chaos in Lorenz Model And Elliptical Billiard Table

     物基一班　 张志城　2013301110121

• 作业L1 3.26
• 作业L2 3.29 3.31
• 作业L3 将以上题目使用vpython进行一个3D展示

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Abstract：
　　In this passage I solve the Lorenz equations using Euler method,and research how this system reaches chaotic state and the phase space of it .Then I simulate the behavior of a ball bouncing in an elliptical billiard table.I use Vpython to demonstate the 3D visual of both systems.

Background
　　The atmospheric scientist E.N. Lorenz was studying the basic equaitons of fluid mechanics,which are konwn as the Navier-Stokes equations.Because the equations were difficult to solve at that time,Lorenz considered a greatly simplified version of the Navier-Stokes equations as applied to particular problems.He grossly oversimplified the problem as he reduced it to only three equations: