[dwattttt]

> By "left out", I mean that there are multiple solutions to the equations of motion which are compatible with the initial values of the situation.

It's worth noting the distinction between a model and the thing the model describes. It's not "cheating" to note that while a model could admit multiple solutions only one could be valid in the original system.

In a very specific sense, eliminating the other solutions is still part of solving the model, just with discrete logic rather than e.g. calculus.