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What (who) is Hamiltonian dynamics - definition
FORMULATION OF CLASSICAL MECHANICS IN TERMS OF PHASE SPACE AND HAMILTONIAN FUNCTION
Hamilton's canonical equations; Hamiltonian dynamics; Hamilton's equations; Hamiltonian Function; Hamiltonian function; ℋ; Hamilton's equation; Hamilton's Equations; Hamiltonian Coordinates; Hamiltonian Mechanics; Hamilton's equations of motion; Hamilton equations; Hamiltonian formalism; Hamilton canonical equations; Hamiltons equations; Hamilton function; Canonical equations; Sub-Riemannian Hamiltonian; Hamiltonian (function)
Hamiltonian (control theory)
FUNCTION USED IN OPTIMAL CONTROL THEORY
Current value Hamiltonian; Present value Hamiltonian
The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period.
Hamiltonian (quantum mechanics)
QUANTUM OPERATOR FOR THE ENERGY
Hamiltonian (quantum theory); Hamiltonian Operator; Hamiltonian operator; Quantum Hamiltonian; Hamilton operator; Schrödinger operator; Kinetic energy operator; Potential energy operator
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.
Hamiltonian mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) momenta.
Wikipedia
Hamiltonian mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.
Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.
