Stabilising an Inverted Pendulum on a Cart

animation, 4th order runge-kutta, system of equations

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

explicit euler method, 4th order runge-kutta, ode, Big Bertha, set of odes

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

  Precession of Mercury

space, einstein, gravity, 4th order runge-kutta, angular momentum, fortran, ode, extrapolation, f2py

Computes the precession of Mercury by linear extrapolation.

  General Relativity

space, einstein, gravity, newton, 4th order runge-kutta, angular momentum, differential equation, ode

Discussion of orbits in the Schwarzschild Geometry.

  Roller Coaster

animation, gravity, newton, 4th order runge-kutta, interpolation, cubic splines

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

  Quadrupole Mass Spectrometer

magnetism, 4th order runge-kutta, voltage, electricity

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

  Lagrange Points

space, gravity, newton, 4th order runge-kutta, lagrange

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

  Adaptive Runge-Kutta Methods

explicit euler method, 4th order runge-kutta, embedded runge-kutta pair, trapezoidal method, ode

Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.

  Runge-Kutta Methods

explicit euler method, 4th order runge-kutta, ode

Solving a first-order ordinary differential equation using the Runge-Kutta method.