The 4th order Runge-Kutta method was used to integrate the equations of motion for the system, then the pendulum was stabilised on its inverted equilibrium point using a proportional gain controller and linear quadratic regulator.
Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.
The Time-Dependent Schrödinger equation is solved by expressing the solution as a linear combination of (stationary) solutions of the Time-Independent Schrödinger equation.
A brief introduction to Brownian motion and its connection with diffusion. A system of Brownian particles in 2D is simulated and visualised.
A one-dimensional wave-packet is propagated forward in time for various different potentials.
Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.
This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.