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4B`=E E mathcad/worksheet.xml ( Converted from "Solving Coupled ODEs in Mathcad" created by Ski SlopeThis set of coupled ODEs describes the motion of a frictionless board as it moves down an infinite sloped surface of sinusoidal humps that extend in both the x and y directions. The equation set comes from Edward Lorenz's book "The Essence of Chaos." The D vector gives the derivatives of four functions, which are So you have a system of four equations, with the first two simply stating that the speeds are time derivatives of the positions, and the second two describing the accelerations. So you need to peel off the first two coordinates of your D vector and the last two of the input. Don't worry about q being undefined, the live symbolic calculations will depend on the form of the function only....so D looks like this...... and this is the setup for the numerical solution. I used Rkadapt, since these chaotic paths often turn suddenly, and our chance of tracking the true solution over a long time is improved by the adaptive routine, although as I'm sure Lorenz's book demonstrates, even good routines will drift off the true solution pretty soon.The first column of the solution is the time variable, and the next two are the x and y positions, which, seen from overhead, have this nice "slalom" appearance. lines1106011In PTC Mathcad Prime, since you can combine different plots, you can show the solution as a path on the ski slope by plotting the path as a connected 3D scatter, something like this:This is a more or less head-on view, looking up the x direction. You can see the solution hitting the walls and zigzagging at the bottoms of the valleys.surfacecurve556-6.51 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | OrthographicPK
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