Transcription of Computational Physics using MATLAB®
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Computational Physics using MATLAB®
Kevin Berwick Page 1 Computational Physics using MATLAB Kevin Berwick Page 2 Table of Contents 6 1. Uranium Decay .. 7 3. The Pendulum .. 9 Solution using the Euler method .. 9 Solution using the Euler-Cromer method.. 10 Simple Harmonic motion example using a variety of numerical approaches .. 11 Solution for a damped pendulum using the Euler-Cromer method.. 16 Solution for a non-linear, damped, driven pendulum :- the Physical pendulum, using the Euler-Cromer method.. 18 Bifurcation diagram for the pendulum .. 24 The Lorenz Model .. 26 4. The Solar System .. 28 Kepler s Laws .. 28 Ex Planetary motion results using different time steps ..30 Orbits using different force laws .. 35 Precession of the perihelion of Mercury.. 40 The three body problem and the effect of Jupiter on Earth .. 48 Chaotic tumbling of Hyperion .. 53 5. Potentials and Fields .. 60 Solution of Laplace s equation using the Jacobi relaxation method.
Equipotential contours near a finite sized capacitor.....69 Figure 34.Equipotential surface in region of a simple capacitor as calculated using the SOR code for a 60 X 60 grid. The convergence criterion was that the simulation was halted when …
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