Hamiltonian mechanics

formulation of classical mechanics in terms of phase space and Hamiltonian function

quantum operator for the energy

physical quantity of dimension energy × time

abstract space whose coordinates are the dynamic variables of the studied system

equation in classical mechanics

bilinear differential operation on scalar fields on a symplectic (or, more generally, Poisson) manifold

theorem that time rate of change of density of points in phase space along a Hamiltonian flow line is zero

in differential geometry, a smooth manifold equipped with a closed, nondegenerate differential 2-form

in Hamiltonian mechanics

sets of coordinates which can be used to describe a physical system at any given point in time

property of certain dynamical systems

formulation of quantum mechanics in phase space

Theorem of dynamical systems

result in dynamical systems about the persistence of quasiperiodic motions under small perturbations; partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics

dynamical system governed by Hamilton's equations

set of canonical coordinates

mathematical concept

In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.

simplification of coordinates for an n-body system

vector field associated to a hamiltonian on a symplectic manifold

principle of least length in physics

canonical differential form defined on the cotangent bundle of a smooth manifold

type of system in classical mechanics

mathematical concept

generalization of Hamiltonian mechanics involving multiple Hamiltonians

tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action, generalizing the classical notions of linear and angular momentum

an equation in the Hamiltonian formulation of geometrodynamics

quantization method for constrained Hamiltonian systems with second-class constraints

field theory coupling of charge but not higher moments

function arising in Hamiltonian mechanics

numerical integration scheme for Hamiltonian systems

variation of Atwood's machine incorporating a pendulum