The uploaded worksheet defines a surface.

I would like to code a ball rolling across this surface (and others) starting from an initial position on the surface and an initial velocity tangent to the surface, but I don't know how to do this.

What is the combination of physics (including gravity) and math that accomplishes this task?

Ball-rolling-on-a-surface.mw

In the final plot in this worksheet, the electric field is displayed using blue headless vectors.

Instead, how can the gradient of the dipole's potential field be displayed in field lines?

Dipole_fields.mw

Circular_gears_meshing_blunt_teeth_shape_from_involute_of_circle.mw

My worksheet has suddenly begun producing the following error message when executing legitimate commands:

Error, (in cos) type `SymbolicInfinity` does not exist

Why has this worksheet suddenly begun issuing these mysterious error messages and how can it be restored to working order?

The uploaded worksheet is intended to be an example of the Equal Incircles Theorem, but the incircles displayed are not equal.

What is wrong in the worksheet and how can the error(s) be corrected?

Equal_Incircles_theorem.mw

I am particularly interested in a full coordplot3d display for ellipsoidal coords.