## 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.