Search: newton

13 results

Astrophysics 2

  Gravity Assist

newton, animation, semi-implicit euler method, gravity

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

  General Relativity

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

Discussion of orbits in the Schwarzschild Geometry.

Root Finding 1

  Fixed-Point Iteration

Newton-Rhapson, method

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

Mechanics 2

  Roller Coaster

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

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

  The Cavendish Experiment

cavendish, curve fitting, harmonic oscillator, newton, gravity

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

Quantum Mechanics 1

  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.

Waves and Acoustics 1


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

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

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 1

  Verlet Integration


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

Root Finding 1

  Newton-Raphson Method


Determining a root with the Newton-Raphson algorithm.