rigid_body_ode_test

rigid_body_ode_test, a MATLAB code which calls rigid_body_ode(), which solves the ordinary differential equations (ODE) representing the Euler equations for a rigid body with three unequal moments of inertia, originally proposed by Fred Krogh.

Licensing:

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

Related Data and Programs:

rigid_body_ode, a MATLAB code which solves the ordinary differential equations (ODE) representing the Euler equations for a rigid body with three unequal moments of inertia, originally proposed by Fred Krogh.

Source Code:

• rigid_body_ode_test.m, calls all the tests.
• rigid_body_ode_test.sh, runs all the tests.
• rigid_body_ode_test.txt, the output file.

• backward_euler.m, a backward Euler ODE solver.
• rigid_body_backward_euler.m, solve using backward euler() method.
• rigid_body_backward_euler_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_backward_euler_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_backward_euler_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_backward_euler_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• euler.m, an Euler ODE solver.
• rigid_body_euler.m, solve using Euler's method.
• rigid_body_euler_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_euler_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_euler_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_euler_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• midpoint.m, a midpoint ODE solver.
• rigid_body_midpoint.m, solve using midpoint().
• rigid_body_midpoint_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_midpoint_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_midpoint_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_midpoint_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• rigid_body_ode15s.m, solve using ode15s().
• rigid_body_ode15s_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_ode15s_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_ode15s_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_ode15s_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• rigid_body_ode23.m, solve using ode23().
• rigid_body_ode23_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_ode23_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_ode23_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_ode23_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• rigid_body_ode23s.m, solve using ode23s().
• rigid_body_ode23s_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_ode23s_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_ode23s_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_ode23s_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• rigid_body_ode45.m, solve using ode45().
• rigid_body_ode45_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_ode45_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_ode45_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_ode45_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• rk4.m, a Runge Kutta order 4 ODE solver.
• rigid_body_rk4.m, solve using Runge Kutta 4.
• rigid_body_rk4_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_rk4_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_rk4_conservation_h1.png, the conserved quantity x^2+y^2+z^2.
• rigid_body_rk4_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.

• trapezoidal.m, a trapezoidal ODE solver.
• rigid_body_trapezoidal.m, solve using trapezoidal().
• rigid_body_trapezoidal_plot.png, time plot of x(t), y(t), z(t).
• rigid_body_trapezoidal_fsolve_phase.png, a 3D plot of (x(t), y(t), z(t)).
• rigid_body_trapezoidal_conservation_h1.png, plots the conserved quantity x^2+y^2+z^2.
• rigid_body_trapezoidal_conservation_h2.png, the conserved quantity x^2/i1+y^2/i2+z^2/i3.