Where is der(v, N) defined?

[casella]

The Modelica grammar has:

result-reference :
   component-reference
   | time
   | der "(" ( component-reference | time ) [ "," UNSIGNED-INTEGER ] ")"

which is also referred to in Section 18.5.2.3.

However, the definition of Operator 3.11 der in Section 3.7.4 just says:

der(𝑒𝑥𝑝𝑟)
The time derivative of 𝑒𝑥𝑝𝑟. If the expression 𝑒𝑥𝑝𝑟 is a scalar it needs to be a subtype of Real.

I guess this should be updated, explaining the meaning of the optional second integer input of the operator.

[HansOlsson]

The goal with adding the syntax der(x, 2) in section 18.5.2.3 was only to make it useful in that place, not as a general second-order derivative operator.

We could, of course, generalize the normal derivative-operator in the same way - but the downsides with describing models in terms of higher order derivatives is that it is more complicated to describe the initialization as there's no variable with a start-attribute (obviously that doesn't matter for the result-file), and that it often looks less clear.

[HansOlsson]

So, to answer the subject-line: der(x, 2) is sort of defined in 18.5.2.3 where result-reference is used, but it could be clearer.

[casella]

We could, of course, generalize the normal derivative-operator in the same way - but the downsides with describing models in terms of higher order derivatives is that it is more complicated to describe the initialization as there's no variable with a start-attribute (obviously that doesn't matter for the result-file), and that it often looks less clear.

I'm well aware of the downsides. Unfortunately, it's the same downsides of using der(der(x)), which I understand is legal, since der(expr) is valid as long as expr is differentiable. Or do I miss something?

Anyway, I understand der(x, 2) can be used in results files in lieu of der(der(x)), but not in the Modelica source code. Do I understand correctly?

[casella]

but it could be clearer.

Current text:

If x or y is a derivative, der(v, n), then n must not exceed the maximum amount of differentiation applied to v in the model.

Proposal:

If x or y is a derivative, der(v, n) (meaning the n-th derivative of v), then n must not exceed the maximum amount of differentiation applied to v in the model.

[HansOlsson]

We could, of course, generalize the normal derivative-operator in the same way - but the downsides with describing models in terms of higher order derivatives is that it is more complicated to describe the initialization as there's no variable with a start-attribute (obviously that doesn't matter for the result-file), and that it often looks less clear.

I'm well aware of the downsides. Unfortunately, it's the same downsides of using der(der(x)), which I understand is legal, since der(expr) is valid as long as expr is differentiable. Or do I miss something?

Anyway, I understand der(x, 2) can be used in results files in lieu of der(der(x)), but not in the Modelica source code. Do I understand correctly?

Sort of, there's one important difference that should be emphasized:

• In Modelica expressions the first argument (of der) is an expression - primarily to handle der(C*v) and similar cases (I view der(der(v)) as more esoteric).
• For result the first argument is a variable, so you cannot write der(C*v) or der(der(x)).

Obviously both of these could be generalized, but I don't see much pressure for that.

[HansOlsson]

Language group:

1. Add reference from der to other one -> @henrikt-ma
2. Could discuss having result-references to expressions and not only variables. (But later; units are more important - and also adding an offset in an expressions is sort of unit-dependent.)

[henrikt-ma]

I plan to do this after #3863 has been merged.