@Rouben Rostamian  Thank you for this recommendation. I was impressed along with Carl Love.

Page 85 in the book Why cats land on their feet introduces the case of a person walking on a rotating platform.

My worksheet animates the differential equation describing this situation on pages 183 and 184.

Unfortunately the author, Mark Levi, does not describe the path taken by the walking person except to infer that he/she is doing so at a constant, unstated velocity.

The motions shown in the youtube video are more interesting. It would ilike to see the development of equations determining the ball's various motions. 

@Carl Love Can a cylinder or a sphere such as you cite be self propelled in any way? If not, then the worksheet must stay unmodified.

@dharr Useful info;- Thank you.

@Carl Love Thanks for the quick reply!

@dharr Your suggestion would save a lot of computation. Thanks for this.

@Ronan Thank you for your attention and your reference. I'm afraid the contents of the paper you referenced is far over my head. However I will continue to explore this subject. 

@Carl Love From the referenced text by Brannan et. al.;

(The procedure rho) is the hyperbolic reflection (of point z) in the hyperbolic line that is part of a Euclidean circle with centre alpha.

How can the Mobius transformation in rho calculate a hyperbolic reflection of a point without requiring input of a radius of the circle referred to? Are not both a centre and a radius required to define the hyperbolic line of reflection?

My procedure InversePtMobius does require both of these inputs and only reproduces the output of procedure rho when InversePtMobius a centre of alpha and a radius of 1. This is why it seems to me that procedure rho assumes a radius of 1. 

*** I just realized that any given centre of the circle mentioned above implies its radius under the condition that the circle meets the Poincare disk at right angles. ***

I therefore withdraw my Maple Primes question

@Thomas Richard 

@mmcdara I have examined your reply to my question and admire your logic.

I have one question.

Apparently the correct animation requires that the pursuer velocity V__P be a specific ratio of the target velocity V__T.

I tried executing the logic using a slightly different ratio and the pursuers stopped short of capturing the target.

Why this specific ratio required and how did you find it?

@Rouben Rostamian   I would award your and mmcdara's answers both with the trophy, I am greatly impressed with both of them!

@mmcdara I would award your and Rouben's answers both with the trophy, they  both are so clever.

@Rouben Rostamian  

@Carl Love 

@Carl Love and to dharr,

Apparently Maple Primes only allows one reply if I my first view of answers includes two of them.

To dharr: Your answer gives me the incentive to begin learning GraphTheory about which I currently know nothing. I am grateful for this.

To Carl Love: Over the years, among all the experts, it seems to me that your answers show the deepest knowledge of Maple's capabilities. I will strive to understand and benefit from this one. I regret I could not also select your answer at the best one.

@acer Both of your methods are enlightening for me. I will study them further. Thank you for this.