HP-41 Module: CHAOS-101

[Ángel Martin]

CHAOS-101 Module

As its name implies, this new 4k-module includes a set of routines and applications dealing with a first-level approximation to chaotic systems. This intriguing subject has grown in popularity in the last couple of decades but wasn’t much of a trending topic when the HP-41 reigned supreme in the calculator world – thus the conspicuous lack of material in the HP-41 literature.

The module is divided in four mayor sections as follows:

1. “-CHAOS-101” is the opening section with a few MCODE utility functions on the subject. Some are trivial examples but nevertheless they’re helpful to understand the basic concepts dealt with in the module. Includes functions on the Logistics Map and the Hénon attractor.

2. Next follows the “-PENDULUM” section, which starts with a large-angle compatible version for the period of a single pendulum, and continues covering the double pendulum, the elastic pendulum, and a 3-magnet configuration of the magnetic pendulum as well. All cases are solved numerically using a 4th order Runge-Kutta method on a system of four ODEs. A set of MCODE functions is also provided to calculate the Lagrangian for any dynamic configuration of these systems.

3. The “-ATTRACTORS” section includes routines to study four of the more popular cases, such as the Lorenz, Rössler, Thomas and Sprott’ systems of three ODEs; also solved numerically using a 4th order Runge-Kutta method. All systems of differential equations have been programmed as MCODE functions for increased accuracy and speed – albeit as you can already expect, “fast” is not a word that defines the operation of the routines. Using TURBO mode (on the 41CL or V41) is a real must.

4. Finally, the “N-BODY PRB” section includes two methods to solve the gravitational n-body problem defined on an inertial frame of reference, using Runge-Kutta and Numerov’s methodology. This section is a subset of the module with the same name, which also includes Heliocentric coordinates and adds a third resolution approach (7-th. degree Multi-step ).

It’s important that you adjust your expectations up front: you’ll find no fancy phase diagrams or 3D representations of the equations of movement in the manual or done with the module – that’s not the point of this project, as it “just” handles a modest numerical resolution of the system equations. No more, no less!

Enjoy!

PS.- Library#4 required, also included in the ZIP container attached.