13 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.

Projectile motion

Computing the trajectory of a projectile moving through the air, subject to wind and air drag.

Precession of Mercury

Computes the precession of Mercury by linear extrapolation.

General Relativity

Discussion of orbits in the Schwarzschild Geometry.

Roller Coaster

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

Cubic Splines

Uses cubic splines to interpolate a given set of data points

Electromagnetism 1

Using numerical tools to describe and analyse a quadrupole mass spectrometer.

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.

Lagrange Points

Studying how a third mass behaves in the effective gravitational potential resulting from two opposing masses (here: Sun and Earth).

Planetary Motion

Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.

Polynomial Interpolation

Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.