@one man 

Hello everyone!

Thank you very much for all the explanations, observations and advice. Thank you very much for the attached Maple source files regarding the issue under consideration. As far as my skills allow, I will try to use them in my work with Maple.

Best regards!

@one man Thank you, I'm thinking about rolling a curve in the third dimension. It's doable, but the difficulty lies in the large number of complex calculations. I even made a simple demo, but Maple is giving me a hard time, which can take away my desire to continue working. In a word, I'll try.

Warmest regards!

@C_R Indeed, there are some calculations, you can reduce the number of frames in the animation, turn off additional calculations, or optimize the way of calculations. I will try to do it.

@Carl Love Thanks for the explanation, I must have made a mistake in my calculations.

Best regards!

@acer Thank you for the explanation, I must then look into the correctness of the previous calculations from which this equation results.

Best regards!

@acer Thank you very much for explaining the method. Now it's a bit more clear. Although at the beginning... The method is very fast, and has a very condensed form. However, after your explanations, I already have a bit more understanding of the subject. This is the first time I've encountered such an approach to solving complex algebraic equations. Thank you very much for this instructive explanation!

@acer Thank you for this solution. Maple is indeed a powerful tool, although the method presented is not easy and requires in-depth knowledge of the Maple environment. Thank you very much! Valuable example!

@vv Now I understand. Thank you very much!

@vv 
Can I ask you to explain in a few words how the code works?
I don't understand the connection between dsolve and fsolve.

@vv

This is beautiful solution. I would never have guessed that you could approach solving this type of equations in this way. It is a very elegant method. Thank you very much for this lesson. I have regained my faith in Maple.

Thank you very much!

Warmest regards!

@Carl Love
Thank you for the correction and explanation of the concept. Time flies, and I haven't dealt with integral equations for a long time. I also thank you for your interest and all the help in finding a methodology for solving this type of equations. I tried in various ways, but I couldn't implement the right method. I certainly don't know it. I wish you a good rest!

@janhardo 

Hello,

All animations work in Maple 2024. Try it and see for yourself.

By the way, I'm posting the last set of DiffGeo procedures, I also changed the procedure calls a bit.

Regards.

clsdgproc_cur&sur.txt

Hello,

Attached is the completed diffgeo procedures and Maple worksheet containing the animation below.

Regards.

Rolling_circle_on_surface.zip

@acer Thank you for the information.

@Rouben Rostamian  

Your code also works on any type of graphics, png..gif.
Thank you very much for helping me!

I greet you very warmly!