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The 59 pages that link to Hamiltonian mechanics, each with the reason it gives.

• Statistical mechanicsRelated: The Hamiltonian specifies energies and dynamics used to construct classical statistical ensembles.

• Conservation of energyRelated: A time-independent Hamiltonian is conserved along a system’s motion.

• Classical mechanicsRelated: It recasts dynamics in phase space and underlies later theories.

• Celestial mechanicsRelated: It provides powerful tools for analyzing stability and long-term orbital evolution.

• Initial-value problemRelated: Hamilton's equations evolve a state forward from specified initial coordinates and momenta.

• Conservation lawRelated: Its equations show how conserved quantities remain constant along a system's evolution.

• Calculus of variationsRelated: It is related to the Lagrangian variational formulation through a change of variables.

• Equipartition theoremRelated: The theorem applies to independent quadratic terms in a classical Hamiltonian.

• Smooth manifoldRelated: Its phase spaces are smooth manifolds equipped with symplectic structure.

• Principle of least actionRelated: It is related to the action formulation and supports powerful transformations of dynamics.

• Poisson bracketRelated: The bracket expresses Hamiltonian evolution as the bracket of an observable with the Hamiltonian.

• Joseph LiouvilleRelated: Liouville studied the preservation of volume in phase space for Hamiltonian systems.

• Legendre transformRelated: The Hamiltonian is obtained from the Lagrangian by transforming velocities into conjugate momenta.

• Lie bracketRelated: Poisson brackets express the time evolution of observables in this formulation.

• Time-reversal symmetryRelated: Time reversal changes momenta while testing whether the equations of motion remain invariant.

• Carl Gustav Jacob JacobiRelated: Jacobi recast mechanics through differential equations and variational principles.

• Symplectic geometryRelated: Its equations of motion are encoded by the symplectic form and a Hamiltonian.

• Jacobi identityRelated: The Poisson bracket's Jacobi identity supports consistent evolution of observables.

• Siméon Denis PoissonRelated: The Poisson bracket became a central structure in this formulation.

• Conserved quantityRelated: Its equations reveal which functions remain constant along a system's trajectories.

• Classical physicsRelated: It expresses classical dynamics in a framework later shared with quantum theory.

• Flow (mathematics)Related: Hamiltonian functions generate flows that describe conservative mechanical motion.

• Linear response theoryRelated: The perturbation is commonly introduced as a change to the Hamiltonian.

• MechanicsRelated: It recasts dynamics in phase space and bridges classical and quantum theory.

• Vladimir ArnoldRelated: Arnold used its geometric structure to investigate stability and long-term motion.

• Poincaré–Birkhoff theoremRelated: Its time evolution produces area-preserving maps and motivates applications of the theorem.

• Theoretical mechanicsRelated: It recasts motion as evolution through phase space.

• Vlasov equationRelated: Hamiltonian particle motion supplies the phase-space flow used in collisionless transport.

• 0-dimensional systemsRelated: It describes internal dynamics without requiring a spatially extended medium.

• Evolution (physics)Related: Hamilton’s equations specify continuous evolution through phase space.

• Non-squeezing theoremRelated: Hamiltonian evolution supplies familiar examples of transformations preserving symplectic structure.