Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Action-angle_coordinates> ?p ?o }
Showing triples 1 to 63 of
63
with 100 triples per page.
- Action-angle_coordinates abstract "In classical mechanics, action-angle coordinates are a set of canonical coordinates useful in solving many integrable systems. The method of action-angles is useful for obtaining the frequencies of oscillatory or rotational motion without solving the equations of motion. Action-angle coordinates are chiefly used when the Hamilton–Jacobi equations are completely separable. (Hence, the Hamiltonian does not depend explicitly on time, i.e., the energy is conserved.) Action-angle variables define an invariant torus, so called because holding the action constant defines the surface of a torus, while the angle variables provide the coordinates on the torus.The Bohr–Sommerfeld quantization conditions, used to develop quantum mechanics before the advent of wave mechanics, state that the action must be an integral multiple of Planck's constant; similarly, Einstein's insight into EBK quantization and the difficulty of quantizing non-integrable systems was expressed in terms of the invariant tori of action-angle coordinates. Action-angle coordinates are also useful in perturbation theory of Hamiltonian mechanics, especially in determining adiabatic invariants. One of the earliest results from chaos theory, for the non-linear perturbations of dynamical systems with a small number of degrees of freedom is the KAM theorem, which states that the invariant tori are stable under small perturbations. The use of action-angle variables was central to the solution of the Toda lattice, and to the definition of Lax pairs, or more generally, the idea of the isospectral evolution of a system.".
- Action-angle_coordinates wikiPageID "5435566".
- Action-angle_coordinates wikiPageLength "7304".
- Action-angle_coordinates wikiPageOutDegree "48".
- Action-angle_coordinates wikiPageRevisionID "649834297".
- Action-angle_coordinates wikiPageWikiLink Action_(physics).
- Action-angle_coordinates wikiPageWikiLink Adiabatic_invariant.
- Action-angle_coordinates wikiPageWikiLink Albert_Einstein.
- Action-angle_coordinates wikiPageWikiLink Bohr–Sommerfeld_quantization.
- Action-angle_coordinates wikiPageWikiLink Canonical_coordinates.
- Action-angle_coordinates wikiPageWikiLink Canonical_transformation.
- Action-angle_coordinates wikiPageWikiLink Category:Hamiltonian_mechanics.
- Action-angle_coordinates wikiPageWikiLink Chaos_theory.
- Action-angle_coordinates wikiPageWikiLink Classical_mechanics.
- Action-angle_coordinates wikiPageWikiLink Conservation_of_energy.
- Action-angle_coordinates wikiPageWikiLink EBK_quantization.
- Action-angle_coordinates wikiPageWikiLink Einstein–Brillouin–Keller_method.
- Action-angle_coordinates wikiPageWikiLink Equations_of_motion.
- Action-angle_coordinates wikiPageWikiLink Fourier_series.
- Action-angle_coordinates wikiPageWikiLink Frequency.
- Action-angle_coordinates wikiPageWikiLink Generalized_coordinate.
- Action-angle_coordinates wikiPageWikiLink Generalized_coordinates.
- Action-angle_coordinates wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Action-angle_coordinates wikiPageWikiLink Hamiltonian_mechanics.
- Action-angle_coordinates wikiPageWikiLink Hamiltons_equations.
- Action-angle_coordinates wikiPageWikiLink Hamilton–Jacobi_equation.
- Action-angle_coordinates wikiPageWikiLink Integrable_system.
- Action-angle_coordinates wikiPageWikiLink Isospectral.
- Action-angle_coordinates wikiPageWikiLink KAM_theorem.
- Action-angle_coordinates wikiPageWikiLink Kepler_problem.
- Action-angle_coordinates wikiPageWikiLink Kolmogorov–Arnold–Moser_theorem.
- Action-angle_coordinates wikiPageWikiLink Laplace–Runge–Lenz_vector.
- Action-angle_coordinates wikiPageWikiLink Lax_pair.
- Action-angle_coordinates wikiPageWikiLink Lax_pairs.
- Action-angle_coordinates wikiPageWikiLink Old_quantum_theory.
- Action-angle_coordinates wikiPageWikiLink Parabolic_coordinates.
- Action-angle_coordinates wikiPageWikiLink Perturbation_theory.
- Action-angle_coordinates wikiPageWikiLink Planck_constant.
- Action-angle_coordinates wikiPageWikiLink Plancks_constant.
- Action-angle_coordinates wikiPageWikiLink Schrödinger_equation.
- Action-angle_coordinates wikiPageWikiLink Spherical_coordinate_system.
- Action-angle_coordinates wikiPageWikiLink Spherical_coordinates.
- Action-angle_coordinates wikiPageWikiLink Superintegrable_Hamiltonian_system.
- Action-angle_coordinates wikiPageWikiLink Tautological_one-form.
- Action-angle_coordinates wikiPageWikiLink Toda_lattice.
- Action-angle_coordinates wikiPageWikiLink Torus.
- Action-angle_coordinates wikiPageWikiLinkText "Action-angle coordinates".
- Action-angle_coordinates wikiPageWikiLinkText "action-angle coordinates".
- Action-angle_coordinates hasPhotoCollection Action-angle_coordinates.
- Action-angle_coordinates subject Category:Hamiltonian_mechanics.
- Action-angle_coordinates hypernym Set.
- Action-angle_coordinates type Mechanic.
- Action-angle_coordinates type Physic.
- Action-angle_coordinates comment "In classical mechanics, action-angle coordinates are a set of canonical coordinates useful in solving many integrable systems. The method of action-angles is useful for obtaining the frequencies of oscillatory or rotational motion without solving the equations of motion. Action-angle coordinates are chiefly used when the Hamilton–Jacobi equations are completely separable.".
- Action-angle_coordinates label "Action-angle coordinates".
- Action-angle_coordinates sameAs m.0dlrm1.
- Action-angle_coordinates sameAs Переменные_действие_—_угол.
- Action-angle_coordinates sameAs Канонічні_змінні.
- Action-angle_coordinates sameAs Q1000646.
- Action-angle_coordinates sameAs Q1000646.
- Action-angle_coordinates sameAs 作用量-角度坐标.
- Action-angle_coordinates wasDerivedFrom Action-angle_coordinates?oldid=649834297.
- Action-angle_coordinates isPrimaryTopicOf Action-angle_coordinates.