• 作业 4.7 4.9 4.11

Homework 11 - The Solar System

ComputationalPhysics_HW 岳绍圣2013301020033

CONTENT:

• Homework 11 - The Solar System
  • Abstract
  • Background
  • The Solar System
  • Codes
  • Reference

Abstract

This article call a model for a nonlinear, damped, driven pendulum. And shows the particular properties that not exists in simple pendulum——chaos. we also changed a small amount of initial conditions, and found a exponential change afterwards. Poincare section is plotted to identify the chaos state. Also, bifurcation diagram is given to show the transistion from nonchaos to chaos.

Background

"Friction" in system always obscures the fundamental physical principles that dominate the behavior of the system we study. So a system without friction, or with small friction is needed to figure out the essential consequences of these peinciples. And we choose the Solar system here.

Our goal is to calculate the position of Earth as a function of time.

The Solar System

This program is heavily commented to provide a detailed explainiation of the purpose of each line of code. This particular simulator uses the Euler method of approximating solutions to the ODEs for the motion of the planetary bodies.

The force each body feels is calculated at each timestep using Newton's law of universal gravitation, which is then used to determine acceleartion. Then, using Euler's method, we are able to approximate velocity and position in a manner that appears realistic.

Codes

All these codes used can be found in Github.

Reference

1: Cai Hao. https://github.com/caihao/computational_physics_whu.
[2]: Nicholas J.Giordano, Hisao Nakanishi.Computational physics.清华大学出版社