Computational Modeling and Visualization of Physical Systems with Python

Contents

1 Introduction

1.1 Computational modeling and visualization

1.2 The science and art of numerics

1.3 Fundamentals of programming and visualization

1.4 Exercises and Projects

1.A Floating point representation

1.B Python installation

1.C The Matplotlib plot function

1.D Basic NumPy array operations

2 Free fall and ordinary differential equations

2.1 Free fall with Euler's method

2.2 The Runge-Kutta methods

2.3 System of first order ODEs

2.4 The leapfrog method

2.5 Exercises and Projects

2.A Area preservation of the leapfrog method

2.B Program listings and descriptions

3 Realistic projectile motion with air resistance

3.1 Visualization of ideal projectile motion

3.2 Modeling air resistance

3.3 Linear air resistance

3.4 The Lambert W function

3.5 Quadratic air resistance and spin

3.6 Physics of ball sports

3.7 Shooting methods

3.8 Exercises and Projects

3.A Bisection and Newton's root finders

3.B Program listings and descriptions

4 Planetary motion and few-body problems

4.1 Motion of a planet

4.2 Properties of planetary motion

4.3 Precession of Mercury

4.4 Star wobbles and exoplanets

4.5 Planar three-body problems

4.6 The restricted three-body problem

4.7 Exercises and Projects

4.A Rotating frames and rate of change of vectors

4.B Rotation matrices

4.C Radial velocity transformation

4.D Program listings and descriptions

5 Nonlinear dynamics and chaos

5.1 A first model: the logistic map

5.2 Chaos

5.3 A nonlinear driven oscillator

5.4 The Lorenz flow

5.5 Power spectrum and Fourier ...