Gravity Assist

animation, gravity, newton, semi-implicit euler method

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

  General Relativity

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

Discussion of orbits in the Schwarzschild Geometry.

  Fixed-Point Iteration

method, Newton-Rhapson

Solving fixed-point problems using the Fix-Point Iteration method.

  Roller Coaster

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

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

  The Cavendish Experiment

gravity, newton, harmonic oscillator, cavendish, curve fitting

Analyzes data from the Cavendish experiment using curve fitting. The Gravitational Constant is estimated.

  Band Structures and Newton's Method

schrödinger equation, bloch's theorem, newton's theorem

Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.

  Sloshing

simpson's method, newton, euler, eigenvalue, poisson's equation, integration, interpolation

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

  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.

  Polynomial Interpolation

newton, lagrange, interpolation, chebychev nodes, runges phenomenon

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

  Verlet Integration

ode

Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.

  Newton-Raphson Method

newton

Determining a root with the Newton-Raphson algorithm.