Part II Computational Physics Projects 2021

Project A: Tidal tails and Saturn's Rings

Project B: The Trojan Asteroids

Exercise 1: Non-linear pendulum

m\,l^2\frac{{{\mathrm d^2}\theta}}{{{\mathrm d}t}^2} = -m\,g\,l\,\sin(\theta) -\alpha\,l\,\frac{{{\mathrm d}\theta}}{{{\mathrm d}t}} +G\sin(\Omega_D t)

Exercise 2: Integration & vectorisation

\int_0^{s} \int_0^{s} \int_0^{s} \int_0^{s} \int_0^{s} \int_0^{s} \int_0^{s} \int_0^{s} \sin( x_1+ x_2+ x_3+ x_4+ x_5+ x_6+ x_7+ x_8) {{\mathrm d}x_1} {{\mathrm d}x_2} {{\mathrm d}x_3} {{\mathrm d}x_4} {{\mathrm d}x_5} {{\mathrm d}x_6} {{\mathrm d}x_7} {{\mathrm d}x_8}

s=\frac{\pi}{8}

where

C(u) = \int_0^u \cos( \frac{ \pi \, x^2}{2} ) \, {{\mathrm d}x}

S(u) = \int_0^u \sin( \frac{ \pi \, x^2}{2} ) \, {{\mathrm d}x}