@WD0HHU 

I got notification of your reply!

Yesterday night I found an option in Outlook to whitelist the adress mapleprimes@maplesoft.com. Just in case, I also whitelisted the domain. (I also changed in Ordering sequence of replies in MaplePrimes)

Thank you!

@one man 

No problem. Currently I also do not get notifications.

The right hand side of the ode's are still a bit opaque to me. In particular the division by sqrt(b[5] ^2+ b[6]^2). Why these two? What makes them special?

I found in Maplesofts application center a good explanation of Draghilev's method from @rlopez  that clarrified a lot. However, for the case discussed there I do not see a division.

Overall, I'm still looking for a good classification of the method. I wouldn't say that I can't see the wood for the trees, but I clearly miss a helicopter perspective that allows me to choose a suitable method for a particular problem.

 @rlopez @Carl Love @Ronan 

New observation: Whenever submenus have disappeared, the plot tool bar (when a plot is selected)  

is not displayed.

Other than that, I have stopped searching for a work around to force recovery of submenus. Maple recovers after a while when the above-mentioned programs run in parallel (after system wake-up from either hibernation or energy-saving;  both triggered by the system with the timings given above).  I could not check systematically whether the other programs needed to be actively used. I also had no time to only run Maple to see if Maple recovers by itself (while working only with Maple).

However, I made an interesting observation. I had a look for other programs that are developed under Eclipse which also suffer from disappearing submenus. The search was unsuccessful but I remembered that MapleSim is also developed under Eclipse and has submenues. Since than I run MapleSim in parallel to Maple 2023 and Maple 2024.

Hope:

So far in MapleSim's File Menu, submenus always worked when they temporarily disappeared in Maple 2023 and Maple 2024.

And (!!!): A Maple session started within MapleSim does not show dissaprearing submenus and plot toolbar while they dissapeared in Maple. Also the context pannel was never empty.  (FYI: MapleSim allows to attach files to a MapleSim document. These attachments can be opened from MapleSim filemenu). Below is the proof. The Maple session started from MapleSim is shown above the Maple session (not displaying the plotmenu) started from Windows startmenu.

I hope this observation can help identifiying essential differences between the two Maplesoft products that are responsible for the GUI malfunctioning of the current Maple versions. I am happy to beta test.

@nm

Thank you for the detailed answer!

@nm 

I so far had no time issues but what you said makes sense.

Since dsolve does some internal testing (otherwise it could not decide after which method to stop), we can assume that each result has been tested. From this perspective a separate test does not make sense unless the test is completely different.

Odetest can of course be used to test any solution. Not only dsolve output. But this does not seems to be its main purpose.

You might know: Do other software packages provide a separate test or is this a speciality of Maple?

@Carl Love 

I went back to my worksheet and converted Math Input back an forth. In Math 2D back ticks are required if a question mark is used in a name. Otherwise the rest of the input after the character before the first questionmark is discarded

This is analogeous to #

Seems that ? can be used in 2D as a single line comment. This does not convert to 1D.

How to run the attachment? Maple evaluates for a long time

Not sure what you mean by basins. This could help you generating a x,y,z plot:

https://www.mapleprimes.com/posts/226664-Exploring-Nonlinear-Dynamics-Analysis

@Paras31 

odeplot uses plot3d,options which do not have a linecolor option. It seems that line coloring is only possible with DEplot.

@mmcdara @one man 

The circle of the maximum radius should be centered on

x2=x1

This assumption makes the search for a solutions much easier. A propper proof of this assumption is a different story. I think it should be possible by starting with a minimized ellipspe at the origin that is subsequently expanded. A differnt way to proof this would be "morphing" of a circle to the ellipse in the drawing above. This will not change the outer two contact points.

The curvature of the circle is always greater than the one of the outer envelope. The limiting curvature of the circle between one and two contact point is the curvature of the outer envelope on the diagonal. Algorithms might be sensitive to this border case.

This code is easier to understand than your former post.
I still don't understand where the b[i] are comming from and what they do.

I also look for a movitation why ode's are generated instead of solving algebraic constraints directly. Is it for the reason that the numerical integration points to the next disrecte solution whereas solving requires selecting a root and deriving algebraic constraints in the first place?

@rlopez @Carl Love @Ronan 

After a week of careful observing in total 3 Maple sessions on two notebooks I see a strong pattern.

This is the process tree from above. (What changed (which is probably irrelevant) is that the two Maple session are now not sub tasks of explorer.exe any more. I assume something restarted the explorer.)

The pattern:

Each time the system hibernates or goes to energy saving the submenus are gone. After a while (~5-10 minutes) working with the system, submenus are back. Applications running in parallel were Outlook, Word, Excel, Teams, Foxit reader, Signal, Firefox and Edge.

Since the moment when the menus came back was not clear, I positioned the Maple 2023 session in the upper right corner of my screen and the Maple 2024 session in the lower right corner (using the Windows key and cursor arrows). In the left half of the screen, I ran the other applications. This permitted me to check the Maple sessions more frequently without opening and closing windows (which might have an impact on the recovery).

Subsequently I closed the applications (I had to kill Teams and Edge in the task manager) up to the point that only Firefox was running in parallel. This did not change the recovery pattern (I.e., this leaves Firefox as one potential reason for recovery).

I also observed that the Maple 2023 session recovered earlier. A reason could be that I configured the system in a way that javaw.exe of Maple 2023 was only running on the internal graphic adapter whereas for Maple 2024 the system was free to choose between internal and external (Nividia) graphics adapter.

Often the context panel was empty when the submenus were gone but not always.

On both notebooks I opened and closed plenty of Maple documents from other authors in the sessions.

The other system only running Maple 2024 without hibernation (only energy saving) showed the same behavior.

Both systems turned on screen saver after 5 min and energy saving after 10 min. Hibernation was activated on one system after 30 min.

There is not much left that I can do to identify an event that triggers recovery.

To further narrow down the root cause, it would now be good,

• that someone can confirm whether there are installations where submenus never come back
• that someone can tell if Linux or Apple systems also show the effect
• if there are Windows 10 installations with a non NVIDIA graphic adapter showing the effect

What Maplesoft could do now: Try to reproduce the above and run a screen recorder while working. It is almost impossible to capture the moment of recovery (context panel of a newly opened document (I open in document mode) showing suddenly context) while doing something in parallel. The screen recording could narrow down the moment of recovery to a few seconds which would allow identifying system events and/or processes triggering the recovery.

I hope that the management will allow a few working days to be sacrificed for this. Submenus that do not work are really annoying and hardly acceptable for a commercial product.

@Alfred_F 

The argument of IsDefine is corrupted. You get the same error message without IsDefine. I managed to recover it, but you might want to enter it again.

IsDefinite(Matrix(2, 2, [[-1/4*(2*u + 10)^2/(81 + (u + 5)^2)^(3/2) + 1/sqrt(81 + (u + 5)^2) - 1/4*(-2*v + 2*u - 2)^2/(4 + (v - u + 1)^2)^(3/2) + 1/sqrt(4 + (v - u + 1)^2), -1/4*(-2*v + 2*u - 2)*(2*v - 2*u + 2)/(4 + (v - u + 1)^2)^(3/2) - 1/sqrt(4 + (v - u + 1)^2)], [-1/4*(-2*v + 2*u - 2)*(2*v - 2*u + 2)/(4 + (v - u + 1)^2)^(3/2) - 1/sqrt(4 + (v - u + 1)^2), -1/4*(2*v - 6)^2/(49 + (v - 3)^2)^(3/2) + 1/sqrt(49 + (v - 3)^2) - 1/4*(2*v - 2*u + 2)^2/(4 + (v - u + 1)^2)^(3/2) + 1/sqrt(4 + (v - u + 1)^2)]]));

@Paras31 I like the idea of color coding. Below it a quick attempt where the color alternates every 50 "seconds". (frem is not the best choice because the first period is only 25 s seconds long).

@WD0HHU 

You are welcome. The whole topic is facinating.

I would be interested if you can make events work and if it makes a difference. If I was in the spaceship, I would in any case halt calculations at an event and restart with modified odes.
That's what I did in an answer that I posted here (which I cannot find straight away). I remember also a pro user posting an event version to the same problem in the same thread.

If I had more time I would try so simulate spaceflight with MapleSim just for curiosity. (I would start with Apollo 8, if data is available). MapleSim uses allot of Maple with one difference that scaling methods are provided.

I have not found out what it is and what it is good for. Scaling might be applicable to such problems.

I am still facinated what is possible today and what people did by hand not so long ago. Luckly, today calculations run faster than real time ;-). The film hidden figures shows it nicely how difficult it was at the time. And by the way, the story of Apollo 11 is boring compared to Apollo 8.