@acer 

your insights are always welcome. I do not understand one detail. Why is executing

time[real](assign('P',plot(fr, 0..10, popts)));

a second time about two times faster?

@WA573 

I have no time to have a closer look. You must check all the derivaties one by one.

For debugging purposes I would remove the alias statement and adapt subsequent statements.

Try for example

diff(S(x, t), x)

and see whether the output is what you want.

@Carl Love 

I did not know this

I think the server needs a restart and/or Mapleprimes has a bug. See here: more than than 10 deleted comments. This does not look like a use error.

@Scot Gould 

This is a valuable option.

I have updated a former question of mine with that information. See: How find out what dsolve,numeric returns

Thank you for adding this.

@acer 

It's not about investigating solvers. I'm trying to analyze a mechanical problem. Right now I'm at the stage where I need to determine the tools/skills required before I begin. I have to weigh clean math in spherical coordinates against the extra effort of calculating derived system states that are not part of the variables of the system of odes. These could indeed be intergrals of system variables. -> 2.)

I have limited experience with solving systems of odes but quites some with approaching problems from the wrong angle;-)  Most likely, I will have some follow-up questions. -> 3.)

As for tools, I have more than enough for the mechanical problem. This post has turned into a rich collection of possibilities that I will probably refer to for other applications.
Thanks again!

@nm 

It seems that we both run Maple in the same way. If Maple were a drink, I would say we like it neat. The only difference I see is the natural language package which I installed for a test. I do not use it. I hope timelimit will improve for you with the library change.

@nm 

libnames are the same as in your update. I only have a Physics Update lib. Additionally a Natural language lib and a MapleSim lib.

I do not see a Physics lib (i.e. without update) if it was that what you removed from your libnames.

I also used Maple 2024.2 and Physics version 1824.

However, I am not sure if I understand correctly. Was there additionally to the Physics Update lib a Physics lib that you removed. If so, it could be the reason for discrepancies that we observed on other occasions between our two installations.

This is how the user related libs look like on my machine

You are using VariationalDifferentiation as if it was a Maple command. The output tells that Maple does not know the name

What do you intend to do with it?

@acer 

Thank you for the analysis. Indeed, I intend  to do much more with it than plotting

@Kitonum 

One thing I did not like about my trials was that they effectivley used the operator form of the plot command but showing a variable in the first argument of the plot command. Your variant is much cleaner also in functional notation

plot('r(t)',t= 0..3, size=[1000,400]);

It seems that functional notation inevitably goes hand in hand with quotation marks when using plot

Thanks!

@nm 

I basically have the same setup appart of having less memory (32 Gb) and the fact that your machine is much faster. I could check for the "experiences pack" if you tell me where you did the screenshot.

60 seconds did not have an effect. Maybe you could try shorter 

I will try later during the day on a faster machine.

@TechnicalSupport 

On windows 10 with the latest physics update

@acer 

Maybe the server also needs a restart: I see here more than than 10 deleted comments.