The Fate of Our Universe

space, gravity, ode

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

  Gravity Assist

animation, gravity, newton, semi-implicit euler method

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

  Precession of Mercury

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

Computes the precession of Mercury by linear extrapolation.

  Double Pendulum and Chaos

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

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

  General Relativity

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

Discussion of orbits in the Schwarzschild Geometry.

  Trigonometric Interpolation

discrete fourier transform, interpolation, fft, least squares

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

  Planetary Motion - Three Body Problem

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.

  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).

  Planetary Motion

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.