### Tag: Lagrangian

Classical mechanics in one post

## Classical mechanics in one post

TL;DR – Classical mechanics describes a divergence-free flow of states. The Hamiltonian is the time component of its vector potential. The Lagrangian is the scalar product between the flow and the vector potential. For the longest time I didn’t know what the Lagrangian was and why its integral is minimized along trajectories. A couple of …

Lagrangian mechanics is a subset of Hamiltonian mechanics

## Lagrangian mechanics is a subset of Hamiltonian mechanics

TL;DR – Hamiltonian systems for which two states have the same trajectory $q(t)$ are not Lagrangian. Lagrangian systems are Hamiltonian systems where the velocity is a function $v=v(x,p)$ strictly increasing with respect to momentum (i.e. an increase in momentum yields an increase in velocity). In a previous post we saw how the photon, as a …