arenstorf_ode


arenstorf_ode, an Octave code which describes an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.

Although the orbit should be periodic, and repeats after a time interval of a little more than 17 units, most ODE solvers will have difficulty coming close to periodicity.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

arenstorf_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

arenstorf_ode_test

biochemical_linear_ode, an Octave code which defines a linear biochemical ordinary differential equation (ODE).

biochemical_nonlinear_ode, an Octave code which defines a nonlinear biochemical ordinary differential equation (ODE).

brusselator_ode, an Octave code which defines the Brusselator ordinary differential equation (ODE) system.

double_pendulum_ode, an Octave code which defines the double pendulum ordinary differential equation (ODE).

flame_ode, an Octave code which considers an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.

henon_heiles_ode, an Octave code which solves the Henon-Heiles system of ordinary differential equations (ODE) which model the motion of a star around the galactic center.

humps_ode, an Octave code which solves an ordinary differential equation (ODE) whose solution is a double hump curve.

kepler_ode_test an Octave code which considers an ordinary differential equation (ODE) which models a Kepler two-body gravitational problem.

kepler_perturbed_ode an Octave code which considers an ordinary differential equation (ODE) which models a perturbed Kepler two-body gravitational problem.

lorenz_ode, an Octave code which approximates solutions to the Lorenz system, creating output files that can be displayed by gnuplot.

normal_ode, an Octave code which sets up an ordinary differential equation (ODE) for the normal probability density function (PDF).

oscillator_ode, an Octave code which defines the highly oscillatory ordinary differential equation (ODE).

pendulum_nonlinear_ode, an Octave code which sets up the ordinary differential equations (ODE) that represent a nonlinear model ofthe behavior of a pendulum of length L under a gravitational force of strength G.

pendulum_ode, an Octave code which sets up the ordinary differential equations (ODE) that represent a linear model ofthe behavior of a pendulum of length L under a gravitational force of strength G.

predator_prey_ode, an Octave code which solves a pair of predator prey ordinary differential equations (ODE).

quadex_ode, an Octave code which solves a stiff ordinary differential equation (ODE), whose exact solution is a parabola, but for which errors grow exponentially.

quasiperiodic_ode, an Octave code which sets up a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.

robertson_ode, an Octave code which sets up a system of three nonlinear stiff ordinary differential equations (ODE) characterizing an autocatalytic chemical reaction.

roessler_ode, an Octave code which defines the right hand side of the Roessler ODE system, which exhibits chaotic behavior.

rubber_band_ode, an Octave code which defines and solves a set of ordinary differential equations (ODE) describing a mass suspended by a spring and rubber band, which can exhibit chaotic behavior.

sir_ode, an Octave code which sets up the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.

sphere_ode, an Octave code which sets up the ordinary differential equations (ODE) which model motion on the surface of a sphere.

stiff_ode, an Octave code which considers an ordinary differential equation (ODE) which is an example of a stiff ODE.

string_ode, an Octave code which simulates the behavior of a vibrating string by solving the corresponding initial boundary value problem (IBVP).

three_body_ode, an Octave code which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.

two_body_ode, an Octave code which simulates the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other.

zombie_ode, an Octave code which sets up a system of ordinary differential equations (ODE) for a generalized SIR infection model to simulate a zombie attack, developed by Philip Munz.

References:

  1. Richard Arenstorf,
    Periodic solutions of the restricted three body problem representing analytic continuations of Keplerian elliptic motions,
    American Journal of Mathematics,
    Volume 85, Number 1, pages 27-35, January 1963.
  2. John D Cook,
    The orbit that put men on the moon,
    https://www.johndcook.com/blog/
    Posted 08 February 2020.
  3. Ernst Hairer, Syvert Norsett, Gerhard Wanner,
    Solving Ordinary Differential Equations I: Nonstiff Problems,
    Springer, 1987.

Source Code:


Last revised on 13 November 2020.