added more textrm, first attempt at structure as per #348

[Peter230655]

• Tried to add missing textrm for nicer looks.
• First attempt at a unified structure as per issue Create consistent formatting for all examples in the gallery #348
• had to add lines prevent_print = 0 to avoid nonsense being output, a semicolon did not work.

[Peter230655]

Unsure, how these unsuccessful tests are related to the simulation I pushed.
Error message says something about pause not defined. I did not touch the code, only optical changes.

[Peter230655]

Trying again.

[Peter230655]

I am very unclear about this error about pause

[moorepants]

Can this be applied to #333 ?

[Peter230655]

I have been thinking along a bit different lines for a while, like:
eom = step(t) * eom1 + (1-step(t)) * eom2, where step(t) = 1 for 0 <= t <= t_impact, step(t) = 0 else.
step(t) must be differentiable, for opty to work no problem here.
step(..) is easy to define along the lines of #350, I think.
Like this, one could handle staged problems if initial_conditions(eom2) = states(eom1(t_impact) - but this is not the case with #333.
I will continue my thinking

[moorepants]

I explicitly want to handle the non-defferntiability as a multiphase problem. It is how we solved the skateboard ollie paper here: https://link.springer.com/article/10.1007/s12283-023-00448-y

[moorepants]

The only thing I need for that example to work is to allow the instance constraint to be at a time not specified in advance, which is exactly what you write in the description to this example.

[Peter230655]

I am afraid, my wording is misleading. What I meant was this:
Say, (x, y) is the location of the body.
Then at present, if you want the body to come close to (x0,y0) during its journey you have to specify a time (which may depend on h) when this should happen.
All my hack does is to avoid having to do this. It does not allow an instance constraint of the form
x.func(t_arbitrary) - x0
y.func(t_arbitrary) - y0

[moorepants]

Ok, got it.

[Peter230655]

Ok, got it.

What would be a less misleading description?
Examples-gallery must no mislead users.
I could explicitly mention, that it does not allow "arbitrary_time" instance constraints?

[moorepants]

I think it is fine, once you read the rest of the example it is clear.

[Peter230655]

The linear combination of the two eoms seems to work fine, and gives expected results.
At present however, I have no idea how get the initial speed of the 2nd phase to be e*final speed of the first phase.