Solving Coupled ODEs in PTC Mathcad

A Ski Slope

By Franceso Onorato

This worksheet will:

• Solve a set of coupled ODEs taken from Lorenz's book, "The Essence of Chaos", to describe the motion of a frictionless board as it moves down an infinite-sloped surface of sinusoidal humps 
• Exhibit relevancy for many industries, specifically in academia 
• Perform ordinary differential equations (ODEs), RKadapt, and Runge Kutta 4th order solvers with adaptive time step

This worksheet sets up a set of coupled ordinary differential equations. A matrix of the functions for the x/y positions and velocities is defined.  It's then passed to the RKadapt function.  The x/y positions are plotted with a 3D plot of the sinusoidal humps, marking the trajectory of the board as it travels through the humps. In practical terms, this can be thought of as the motion of a set of skis going down a mountain.  Step by step notation, formulas, equations, graphs, images, and solutions are all provided in this worksheet to aid you.

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