Lagrangian, Newtonian, and Hamiltonian: the same dynamics

What you are seeing: a planar pendulum drawn three ways. Newton: force balance on the bob; tension and gravity are arrows. Lagrangian: a single generalized coordinate $\theta$ and its conjugate velocity; equations come from $L = T - V$. Hamiltonian: $H = p^2/(2mL^2) - mgL\cos\theta$ on a phase plane.