New ModelKind: `EquilibriumModel`?

[balacij]

Related to #2371

Considering SSP's equilibrium TM and momentEql GD, I don't these are models that we can model as EquationalRealms because an EquationalRealm says that some quantity can be defined using one of any number (> 1) expressions. I think we need a new kind of model that says:

• for some pool of expressions, they are equivalent under certain conditions (conditions may be trivial/empty)
• we can calculate settings where the above equivalence holds using a set of QDefinitions that define the variables

Related models:

[JacquesCarette]

Right - I think this one is indeed different. I think it's actually 3 equations (all with rhs 0). It's not correct to say that the first two sums are equivalent! The constraint is that all 3 must be 0.

I don't quite know what to call these. @smiths ? Are these 'conservation' laws? While I understand that they are 'equilibrium' equations, that seems too specific.

EquationalConstraints ?

[smiths]

@balacij, the way equilibrium conditions are written isn't so much to show that the sums of forces and moments are equal; it is just a short-hand notation to show that they are all equal to zero. That is, the important fact isn't that they are equal; the important fact is that they are all equal to zero.

It might help to write the equilibrium condition as three separate equations, each of which is a sum of forces (or moments) that are equal to zero.

The reply for @JacquesCarette just showed up as I was typing this. :smile:

Yes, this is a conservation law. It is a special case of the conservation of momentum, where the momentum is zero. It might be confusing to call it this though, since the concept of momentum isn't needed anywhere else in the problem. We can derive equilibrium from Newton's second law, but that might be making things too abstract.

[balacij]

Perfect!

Would TM consThermE of SWHS also be considered an EquilibriumModel?

Also, the linked source for this one calls a similar equation a "steady state equation". Perhaps SteadyStateModel is a more precise name than EquilibriumModel?

[smiths]

The heat transfer model above isn't an equilibrium model, but a conservation model. In this case it is the conservation of thermal energy. Steady state is used when time isn't part of the model. That is, when things are no longer varying over time. The conservation of thermal energy model is steady state if the term involving the derivative of time is equal to zero.

[balacij]

Ah, thank you @smiths! I'll need to go through this ticket slowly and come back with a fresh set of questions :smile:

[JacquesCarette]

Let's call these EquationalConstraints. I don't think it makes a difference whether there's one or many - they are all implicit equations that will need "real work" before they can be used in code.

They arise from different situations in physics, but none of those is general enough. Here, I think we need to fall back onto the raw mathematics as the way to describe the situation.

[balacij]

That sounds good. I can work on building them today with multiple equations instead of one. Thank you.