@Carl Love 

Your guess in point 5 is correct. There is only one dependent function, phi(t).

I have corrected the ode and ics arrording to C_R 3962 and Reuben Rostamian's suggestions and the original error message has been replaced by the one in dharr's response.

I will try to manually convert to a first-order system.

@dharr 

I have corrected the ode and ics according to C_R 3962's, Carl Love's and Reuben Rostamian's suggestions and the original error has disappeared, however the new error is the one shown in dharr's reply. I will try manually to convert to a first order system according to your suggestion using the correct initial conditions.

@C_R I have corrected the ode and ics according to your and Reuben Rostamian's suggestions and the original error has disappeared, however the new error is the one shown in dharr's reply. I will try manually to convert to a first order system according to his (her?) suggestion

@Rouben Rostamian  You have enlightened me by your insight, as you have done so many times!!

@janhardo With this simple change Maple2020 executes your worksheet without a problem.

I like your display of the magnetic field induced in the wire. Also, the 3D display is more enlightening that the 2D display.

@janhardo Thanks for your quick reply.

Unfortunately when I executed your downloaded worksheet only the opening text displayed. The commands producing the animation did not execute. I presume Maple2020 could not handle your implementation written in a later Maple version.

@dharr Thank you for explaining my programming error.

I moved the ode definition inside the MoveRod procedure and the animation worked perfectly

@dharr The Maple2020 help has given me a good understanding of this form of dsolve. Thank you.

@Rouben Rostamian  

@Rouben Rostamian  I downloaded your worksheet, made changes to adapt it to Maple2020, and executed it.

It is a beutiful answer to my question!

Obviously something is wrong in my question's downloaded worksheet in my interpretation into Maple2020 of the youtube's differential equations. Maybe I can determine my errors.

I deeply appreciate all of the answers you have sent me over the past few years. Thanks again.

@C_R These are interesting. They also solve the problem with a completely different math than in the youtube video reverenced in my worksheet.

I especially enjoyed the history of the problem outlined in the video included in one of your referrals.

@acer Rouben Rostamian's solution to a similar problem is very different from that in the referenced youtube video, but interesting none the less.

Can any other shape pass through a cube while removing more of the cube's volume?

@Kitonum Your procedure is the best way to generate any similar chain of tangent circles. Thank you for this.

@Rouben Rostamian  Thank you, Mr. Rostamian