Solving the Friedmann equations to model the expansion of our universe.

newton, animation, semi-implicit euler method, gravity

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

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

Computes the precession of Mercury by linear extrapolation.

differential equation, animation, Lagrangian, Euler-Lagrange equations, chaos, phase space, odeint

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

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

Discussion of orbits in the Schwarzschild Geometry.

interpolation, fft, discrete fourier transform, least squares

Using trigonometric interpolation and the discrete Fourier transform to fit a curve to equally spaced data points.

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.

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).

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.