@acer That's an accepable work around for technical documentation. Thank you! 

@acer Thanks!

To add to acers answer look at this subtile difference

Numbers in subscripts are rendered in Maple in italic as if they were letters. This is  not following a common layout convention in math that numbers are rendered in roman (if you want this, you have to use indexes).

With eagle eyes it is visible in the output that something is wrong with the displayed input

No, it does not happen with this model.

I assume that you have used an older model.

With respect to math and Maple we have to live with the fact that LLMs do not provide reliable anwers.

To install Maple 2024.1 you need an installer file (MAplesoft only provides the latest version for download). If you have kept this file you could give it a try. In a reply to @nm I once manged to install an older version in parallel to a newer version (I could not find my reply straigh away for more details on that).

CPU usage: 30% is very high. What exactly uses 30%? Could you send a screen shot from the taskmanager

I experience non-responsiveness under the following condition: big files *.mw with graphic ouput (plot structures for animation).

Since 10 Gb of memory allocated is rather big, we need to understand whether the kernel (mserver.exe) or the kernels or the GUI allocates the memory.

Auto save paralyses the GUI. Could this be the reason? Watch the status bar and/or turn auto save off to see if that makes a difference.
Save paralyses the GUI as well (not visible in the GUI that a save operation is ongoing in the background). By paralysing I mean the no keyboard entry is visible altough the cursor can be placed.

The context panel ?worksheet,reference,contextpanel generates output previews. @acer mentionned this a reason. Closing it should stop the generation of previews.

Unusable: Yes, Maple sometimes becomes unusable. Your description is not exagerated. I could workarround this by doing code changes before execution a worksheet after opening and/or deleting graphic output.

Uploading a worksheet is helpfull to reproduce what you are experiencing.

The maximum seems to be at k2=0.

Are you aware of it? If this (k2=0) can be prooved the condition can only be fullfiled for delta=0 which is not a maximum value. That is why "no improved point could be found".

@nm 

I would try to set kernelopts(numcpus=1)

@nm 

Have you tried to run this problem on a single thread or core?

The latest version of Maple shows the behaviour you desire (default folder is set to the location where a double-click is performed). Maybe these settings influence the selection of the default folder

@Rouben Rostamian  

I am aware of the advantages of quaternions but lack experience. Very little to find about them in combination with Maple.

For this reason I was looking for supporting functionality from Maple for something I know (Euler angles).

For one static rotation plottools:-rotate is a step in the right direction. Looks like that a bunch of vectors can be converted with one statement.

For dynamic problems: I have seen that you use quaternions for systems ode's. Very interesting, but I need to get hands on (one day...). 

@Christopher2222 

It was possible to add the contact force to the simulation for this simple case (see attached). Now it is easier to observe the force.

simplified_disk_pendulum_with_force.msim

Note:
If the mass m in the center is set to zero (try the new rerun feature for this. decend to 0.001 and then to zero), the excentric mass is not falling in a straight line. The problem has become unphysical. Change the solver to variable. Then you can approach zero (but not run at zero). All this are signs for an ill-conditionned case.

@Christopher2222 

The fix does not change the behaviour. The behaviour stems from a combination of the "extreme parameters" (i.e. an excentric mass inside a massless contact body without friction but with elasticity in the contact).

Make a thought experiment and try to model this in Maple: It is basically a free falling mass. In the animation of Orang ("hits the wall" here) it looks like that a contact force is only generated when the contact point is between the center of the contact element and the excentric mass. I do not know if this a correct observation and if it makes sense. I have to think about it. (Edit: striked through since the observation was wrong) A contact point and force visualization in MapleSim would be helpfull for an analysis.

The rolling case is much easier to model n Maple

@mmcdara

Thank you so much for all the references. I made this post one of my favourites and added new tags in the hope that others can find it and profit from it as I did.

I have to say it again: The content is worth a post. Proper classification of periodic, quasi-periodic, psuedo-chaotic and chaotic behaviour is less trivial than I thougth.

@nm 

I could not reproduce this pseudo-ramdom error with former versions of Maple.

If you want, I can try it for the new error

@Rouben Rostamian  

Correct: eta is not periodic (at least for small timescales). It could be that after many cycles (stop-and-go's of the big circle) eta has the same value as at the beginning of the simulation. For that a certain ratio of radii and masses is required. Since this is not a celestial motion (or a gear drive), its difficult to tell what rational ratio of numbers is required. I would be surprised if there is no periodic solution at all.

Chaos: The type of chaos I had in mind is an unexpected behaviour. Like here for the double pendulum where the small link changes the sense of rotation while the big link swings back and forth.