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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.

• Newtonian mechanicsCompared with: It describes the same classical motion through an energy-centered mathematical framework.

• Lagrangian mechanicsCompared with: It replaces velocity-based dynamics with phase-space evolution after a Legendre transform.

• Phase spaceBroader topic: Its canonical equations specify the flow of points through mechanical phase space.

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

• Joseph-Louis LagrangeCompared with: Hamilton’s later formulation offers a closely related but distinct route from Lagrange’s equations to motion.

• Virial theoremNarrower topic: Hamiltonian methods express virial relations for systems beyond simple point masses.

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

• KinematicsCompared with: It explains the evolution of physical systems, not merely their motion's geometry.

• 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.

• N-body simulationNarrower topic: It explains why gravitational trajectories and energy conservation guide integrator design.

• 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.

• William Rowan HamiltonBroader topic: Hamilton recast mechanics in terms of energy and canonical variables.

• Canonical quantizationNarrower topic: Canonical quantization takes its variables and dynamics from this classical framework.

• Hamilton–Jacobi equationNarrower topic: The equation is the Hamiltonian formalism's partial-differential counterpart.

• Theoretical physicsBroader topic: Its phase-space structure underlies statistical mechanics and quantum theory.

• Microcanonical ensembleNarrower topic: Hamiltonian dynamics describes the energy-conserving trajectories represented in classical phase space.

• 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.

• Hamilton's principleCompared with: It expresses evolution in phase space rather than deriving it directly from stationary paths.

• KAM theoryNarrower topic: KAM theory is formulated for perturbations of Hamiltonian dynamics.

• Action-angle variablesNarrower topic: Action-angle coordinates are canonical coordinates within this broader framework.

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

• Hamiltonian operatorNarrower topic: The quantum operator develops the energy-generating role of its classical counterpart.

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

• Pierre Louis MaupertuisBroader topic: Its action-based formulation developed a broader mechanics than Maupertuis’s original statement.

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

• Analytical mechanicsBroader topic: It recasts dynamics in terms of coordinates, momenta, and energy.

• Integrable systemNarrower topic: Hamiltonian integrability is defined through conserved functions on phase space.

• Symplectic manifoldNarrower topic: Symplectic geometry supplies the structure behind its equations of motion.

• Adiabatic invariantNarrower topic: Adiabatic invariance is commonly derived for Hamiltonian systems with slowly varying parameters.

• 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.

• Free particleNarrower topic: Its energy function provides the classical counterpart to a quantum free Hamiltonian.

• Paul EhrenfestNarrower topic: The theorem’s quantum averages mirror Hamiltonian equations for position and momentum.

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

• Classical statistical mechanicsNarrower topic: Its equations specify the microscopic dynamics underlying the statistical description.

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