# Hamiltonian mechanics > [[PORTAL_Dynamical_system|Dynamical system]] · [[PORTAL_Decision_theory|Decision theory]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Hamiltonian_mechanics.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Hamiltonian mechanics — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> Hamiltonian mechanics is a reformulation of classical mechanics, introduced by William Rowan Hamilton in 1833, that describes a physical system entirely in terms of position and momentum coordinates evolving according to a single function — the Hamiltonian, usually the system's total energy. Where Newtonian mechanics tracks forces, Hamiltonian mechanics works in phase space and yields Hamilton's equations, a symmetric pair of first-order differential equations for how position and momentum change together. ## Overview This build renders a system's trajectory through phase space live as Hamilton's equations are integrated, letting the characteristic closed or quasi-periodic orbits of a conservative system be watched directly. The Hamiltonian framework is the natural setting for [[Liouville's_theorem_(Hamiltonian)|Liouville's theorem]] — phase-space volume is conserved as a system evolves — and its structure generalises directly to a [[Symplectic_manifold|symplectic manifold]], the geometric object phase space turns out to be. As one of the cleanest examples of deterministic evolution in a well-defined state space, Hamiltonian mechanics is a standard reference point in [[Dynamical_system|dynamical-systems]] theory and in [[Decision_theory|decision theory]]'s optimal-control tradition, where Hamilton's equations reappear as the necessary conditions of Pontryagin's maximum principle for finding an optimal trajectory over time. **On the spine:** [[Dynamical_system]] · [[Decision_theory]] · [[Liouville's_theorem_(Hamiltonian)]] · [[Symplectic_manifold]] · [[Phase_space]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Hamiltonian_mechanics) : [Wikitube](https://en.wikitube.io/wiki/Hamiltonian_mechanics) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*