Ciro Santilli @cirosantilli  40

See: math.stackexchange.com/questions/579453/real-world-application-of-fourier-series/3729366#3729366

The simplest harmonic oscillator system.

The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.

Bibliography:

Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.

Ahh, Ciro Santilli was certain this was some slang neologism, but it is actually Greek! So funny. Introduced into English in the 19th century according to: www.merriam-webster.com/dictionary/kudo.

One, single. Actual word: μόνος.

It is fun to see that C and G have been confused since antiquity:

Confusingly, in LaTeX:

Lower case looks like the mouth shape when you say Z, with mouth open, and you can even see the little tongue going down. Beauty.

Lowercase looks like a lowercase letter N for some reason.