## 10 results

#### Stabilising an Inverted Pendulum on a Cart

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.

#### Gravity Assist

Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.

#### Double Pendulum and Chaos

Discusses the chaotic motion of the double pendulum using a phase-space diagram

#### Simple Pendulum

Simulates the simple pendulum and damped simple pendulum

#### Roller Coaster

The motion of a rolling object on an arbitrary track is analyzed.

#### Solving the Time-Dependent Schrödinger equation

The Time-Dependent Schrödinger equation is solved by expressing the solution as a linear combination of (stationary) solutions of the Time-Independent Schrödinger equation.

#### Introduction to Brownian Motion and Diffusion

A brief introduction to Brownian motion and its connection with diffusion. A system of Brownian particles in 2D is simulated and visualised.

#### One-Dimensional Wave Propagation

A one-dimensional wave-packet is propagated forward in time for various different potentials.

#### Planetary Motion - Three Body Problem

Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.

#### Partial Differential Equations - Two Examples

This module shows two examples of how to discretize partial differential equations: the 2D Laplace equation and 1D heat equation.