The bookUnit 3 · Classical Mechanics69 / 83

Hamiltonian formalism and conservation laws

Why this is asked: H = Σpq̇ − L expressed in (q, p). Poisson brackets test canonicity: {Qᵢ, Pⱼ} = δᵢⱼ, {Qᵢ, Qⱼ} = {Pᵢ, Pⱼ} = 0.

Hamiltonian mechanics, Poisson brackets and canonical transformations

The written notes for this page come with the Notes pack. The video, the visual and the practice below are free.

See it move

The Legendre transform done once, plus the reason a Hamiltonian system can never have an attractor.

The trap here

“The Hamiltonian always equals the total energy” — false

A bead on a wire rotating at forced angular velocity $\omega$

The constraint is time-dependent, so H is conserved but differs from T + V.