The uploaded worksheet references two youtube videos.

The first one displays the animation of a simple device rotating about an axis tilted at a small angle from the device's principal axis having an intermediate moment of inertia.

The animation and accompanying verbal description demonstrate the Dzhanibekov effect.
The second video contains the first video's narrator's equations which produce the values used in creating the animation.

The uploaded worksheet contains my failed attempt to reproduce these values.

Please suggest the Maple 2020 compatible statements which correctly produce these values.

Dzhanibekov_effect.mw

Problem Q15 in the book Parabolic Problems by David Angell and Thomas Britz describes a large circle (LC) and several smaller circles (SCs) which are each tangent to its neighbour SC(s), and externally to LC. All circles are tangent to the x axis and above it.

Section one of this worksheet displays the LC and six of the SCs based on the book's formula for the diameter of the latter in terms of the diameter of the LC and the largest SC, which is determined by the user.

Section two finds and displays that all of the displayed SCs' centers lie on the diameter of a circle closely related to the LC and larger than it.

Can this be proved to be the case for any sizes of the LC and SCs in the same formation as that displayed?

Parabola_Problems_Q15.mw

This worksheet defines two physics problems and fails in the attempt to solve the first one.

How can these problems be solved?

Rolling_circle.mw

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