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You are on the right track. Without fear of breaking Vladislav's "precepts", I can tell you even more.
The quadratic form is a very simple thing and does not contain singularities, discontinuities and so on. Therefore the trajectory exists, even without verification. Minimization is the principle by which the true trajectory is found. The whole question is what to minimise ! If you get to that point, it's really an advancement.
But the question of how to minimise is something which, according to the general agreement, is not subject to public disclosure.
Whoever understands what, why, and for what purpose will think of a way to minimise it.
That's for sure!
That's for sure!
Hi ! Did you find any errors in the output of that formula ?
1. a minimum of potential energy of the channel
2. some minimum of potential energy
3. some trajectory of the price movement
4. the trajectory of the price movement from the potential energy
5. minimum value of the trajectory
6. something else?
I'm sure that if we take time together to formalize the problem statement, things will be more fun. A correctly formulated problem is half the success in its solution (someone from the great ones said so :o). Or am I the only one who doesn't understand what I'm searching for? If so, enlighten me, because reading the forum, I have a double impression of what distinguished participants are trying to calculate.
I did not find any. Especially since it looks like it produces excellent results (RMS definitions).
One sleepless night, that's all... No need to look for U=f(x, y), no need to look for the dependence of price on potential energy. You'll never find it, it's much simpler...
I made up a whole poem :) And you took all found, but I'll probably be glad anyway, if you are right, I hope you hint, if not, I have not been typing in vain and then post my views on the problem ;) (More precisely the purpose of the search)