If we are moving initial conditions to a dedicated module, let's also move the following lines to a dedicated module (maybe model.py or something).

I feel most people won't look into __init__.py unless it is related to __all__.
Maybe we only do imports in __init__.py. Something like

from hamilflow.models.harmonic_oscillator.model import SimpleHarmonicOscillator, DampdHamonicOscillator


__all__ = ["SimpleHarmonicOscillator", "DampdHamonicOscillator"]

I propose to separate engineering and scientific efforts to different issues and MRs, so we can streamline iterations.

More concretely, I propose to merge #56 first, then this #54, and finally the newly created #57.

Now I see what is not compatible with py39... It is expected: dict[str, float]. Should be expected: Dict[str, float], where Dict is imported from typing.

To be honest I am not happy with the syntax system["omega"]. It breaks the design and steals data from the system dictionary. I guess we need to improve the design at some point. @emptymalei

This one looks quite bad. Can we reduce the complexity by settle on one certain kind of convention?

We don't aim to generate a good interface for users to use. As long as we can set the convention for ourselves, I am okay with anyone of the three choices.

Note that $(E, t_0)$ is associated with the first integral of the system. First integrals, or constants of motion, have special and physical meaning in the framework of analytical mechanics. This is in contrast with the phase $\phi$.

Let us sleep over it a bit and then decide.

Note that (E,t0) is associated with the first integral of the system. First integrals, or constants of motion, have special and physical meaning in the framework of analytical mechanics. This is in contrast with the phase ϕ.

Let us sleep over it a bit and then decide.

Can we just keep $(E, t_0)$ and drop the others? I am still not sure how you are gonna use it. But I am okay with any of these choices. But the last thing I want is all of them clustered in a function. It would be easier to just chose one and force it.