The uploaded worksheet describes a mechanics scenario which I would like to animate.

While I understand the expression for the kinetic energy of the torus, the term containing cos(theta) within the expression for the KE of the pearl baffles me.

From which physics aspect of the scenario does this term derive?

Pearl_in_torus.mw

The worksheet below animates the flattening of a tetrahedron by expanding one of its faces, namely its triangular base.

I would like to animate the flattening of an octahedron so that it assumes the 2D figure resembling the Morley triangle which is included in the worksheet.

Are there documents on the web explaining the technique for doing so? Is there a Maple worksheet available on the web demonstrating the desired animation?

Flatten_a_tetrahedron.mw

This worksheet is a modification to Kitonum's excellent http://www.mapleprimes.com/posts/202222-Contour-Curves-With-Labels.

The mod adds the ability to display labelled contours for expressions in x and y defined parametrically.

Your comments are welcome.

Contourplot_with_labels.mw

The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

EllipseRoll.mw

The conditional trigger in the code below does not cause a halt although odeplot shows x dipping to a value below 2.

What is the correct coding of this event to cause a halt when x becomes less than 2?

Does any Maple documentation show examples of working discrete events with conditional triggers?

restart;

DE1 := diff(x(t), t, t) = -x(t)-(diff(x(t), t))+y(t);

DE2 := diff(y(t), t, t) = y(t)-(diff(y(t), t))+x(t);

ICs := x(0) = 2, (D(x))(0) = 1, y(0) = 0, (D(y))(0) = 1;

sol1 := dsolve({DE1, DE2, ICs}, {x(t), y(t)}, numeric, event_initial = true, events = [[[0, x(t) < 2], halt]]);

plots:-odeplot(sol1, [t, x(t)], t = 0 .. 3);