@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!

@acer 

Your solution works perfectly!!! I don't know how to thank you! Thank you very much for your help!

This is what I was missing. I am very grateful to you!

I greet you very warmly!

P.S.

I will test your code on the rest of my code.

Once again, thank you very much!

@acer 

After applying the function:

#**********************************
# MAPLE 18 RESIZE IMAGE *
#**********************************
Resize := proc(P,m::posint,n::posint)
      op(0,P)(op(P),ROOT(BOUNDS_X(0),BOUNDS_Y(0),
                   BOUNDS_WIDTH(n),BOUNDS_HEIGHT(m)));
end proc:

it is impossible to do export with:

plottools:-exportplot(path, rpl);

Where:

rpl := Resize(plots:-display(seq(plotAll(t),t=tRange,step),insequence=true,labels=[x,y,z],labelfont=["TimesNewRoman",16],orientation= [30,30],scaling=constrained),1000,1000);

This cannot be done because rpl is no longer a PLOT3D structure but a function. So if it was possible to restore rpl to the PLOT3D structure, export would be possible. But I don't know how to do it.