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

animation, gravity, newton, semi-implicit euler method

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

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

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

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

discrete fourier transform, interpolation, fft, least squares

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

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

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

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).

space, explicit euler method, gravity, newton

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