While looking through my past H essays I noticed a typo in Hamiltonian, an essay from the 2019 A-to-Z. Every time I look at an old essay I find a typo, even ones I’ve done this for before. Still, I choose to take it as a sign that this is an auspicious choice.
The Hamiltonian is one of the big important functions of mathematical physics. For all that, I remember being introduced to it, in a Classical Mechanics class, very casually, as though this were just a slightly different Lagrangian. Hamiltonians are very like Lagrangians. Both are rewritings of Newtonian mechanics. They demand more structure, more setup, to use. But they give fine things in trade. So they are worth knowing a bit about.