Search: runge

13 results

Mechanics 2

  Stabilising an Inverted Pendulum on a Cart

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

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

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

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

Astrophysics 2

Mechanics 1

  Roller Coaster

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

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

Curve Fitting 1

Electromagnetism 1

  Quadrupole Mass Spectrometer

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

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

Astrophysics 3

  Planetary Motion - Three Body Problem

animation, gravity, newton, embedded runge-kutta pair, angular momentum, space

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

  Lagrange Points

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

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

  Planetary Motion

newton, space, explicit euler method, gravity

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

Curve Fitting 1

  Polynomial Interpolation

chebychev nodes, newton, interpolation, lagrange, runges phenomenon

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

Ordinary Differential Equations 2

  Adaptive Runge-Kutta Methods

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

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

  Runge-Kutta Methods

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

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