squircle_ode

squircle_ode, a Python code which sets up a system of ordinary differential equations (ODE) for a pair of functions that generalize the sine and cosine, and whose phase portrait is a squircle, a sort of squared circle.

Licensing:

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

Languages:

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

Related Data and codes:

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

Reference:

• John D Cook,
  A generalization of sine and cosine,
  https://www.johndcook.com/blog/2020/12/21/generalization-sine-cosine/
• David Shelupsky,
  A generalization of the trigonometric functions,
  The American Mathematical Monthly,
  Volume 66, Number 10, December 1959, pages 879-884.

Source Code:

• squircle_ode.py, the source code.
• squircle_ode.sh, runs all the tests.
• squircle_ode.txt, the output file.

• squircle_midpoint_plot.png, a plot of two solution components over time.
• squircle_midpoint_phase.png, a phase plot.
• squircle_midpoint_conservation.png, a plot of the energy over time.

• squircle_solve_ivp_plot.png, a plot of two solution components over time.
• squircle_solve_ivp_phase.png, a phase plot.
• squircle_solve_ivp_conservation.png, a plot of the energy over time.