Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Laplace–Runge–Lenz_vector> ?p ?o. }
Showing items 1 to 37 of
37
with 100 items per page.
- Laplace–Runge–Lenz_vector abstract "In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be conserved. More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them; such problems are called Kepler problems.The hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse square central force. The LRL vector was essential in the first quantum mechanical derivation of the spectrum of the hydrogen atom, before the development of the Schrödinger equation. However, this approach is rarely used today.In classical and quantum mechanics, conserved quantities generally correspond to a symmetry of the system. The conservation of the LRL vector corresponds to an unusual symmetry; the Kepler problem is mathematically equivalent to a particle moving freely on the surface of a four-dimensional (hyper-)sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher symmetry results from two properties of the Kepler problem: the velocity vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points.The Laplace–Runge–Lenz vector is named after Pierre-Simon de Laplace, Carl Runge and Wilhelm Lenz. It is also known as the Laplace vector, the Runge–Lenz vector and the Lenz vector. Ironically, none of those scientists discovered it. The LRL vector has been re-discovered several times and is also equivalent to the dimensionless eccentricity vector of celestial mechanics. Various generalizations of the LRL vector have been defined, which incorporate the effects of special relativity, electromagnetic fields and even different types of central forces.".
- Laplace–Runge–Lenz_vector wikiPageID "719460".
- Laplace–Runge–Lenz_vector wikiPageRevisionID "605770523".
- Laplace–Runge–Lenz_vector backgroundColour "#F9FFF7".
- Laplace–Runge–Lenz_vector borderColour "#0073CF".
- Laplace–Runge–Lenz_vector cellpadding "6".
- Laplace–Runge–Lenz_vector indent ":".
- Laplace–Runge–Lenz_vector indent "::".
- Laplace–Runge–Lenz_vector subject Category:Articles_containing_proofs.
- Laplace–Runge–Lenz_vector subject Category:Classical_mechanics.
- Laplace–Runge–Lenz_vector subject Category:Mathematical_physics.
- Laplace–Runge–Lenz_vector subject Category:Orbits.
- Laplace–Runge–Lenz_vector subject Category:Rotational_symmetry.
- Laplace–Runge–Lenz_vector subject Category:Vectors.
- Laplace–Runge–Lenz_vector comment "In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be conserved.".
- Laplace–Runge–Lenz_vector label "Laplace-Runge-Lenz-Vektor".
- Laplace–Runge–Lenz_vector label "Laplace-Runge-Lenz-vector".
- Laplace–Runge–Lenz_vector label "Laplace–Runge–Lenz vector".
- Laplace–Runge–Lenz_vector label "Vecteur de Runge-Lenz".
- Laplace–Runge–Lenz_vector label "Vector de Runge-Lenz".
- Laplace–Runge–Lenz_vector label "Vetor de Laplace-Runge-Lenz".
- Laplace–Runge–Lenz_vector label "Vettore di Lenz".
- Laplace–Runge–Lenz_vector label "Вектор Лапласа — Рунге — Ленца".
- Laplace–Runge–Lenz_vector label "拉普拉斯-龍格-冷次向量".
- Laplace–Runge–Lenz_vector sameAs Laplace%E2%80%93Runge%E2%80%93Lenz_vector.
- Laplace–Runge–Lenz_vector sameAs Laplaceův-Rungeův-Lenzův_vektor.
- Laplace–Runge–Lenz_vector sameAs Laplace-Runge-Lenz-Vektor.
- Laplace–Runge–Lenz_vector sameAs Διάνυσμα_Laplace–Runge–Lenz.
- Laplace–Runge–Lenz_vector sameAs Vector_de_Runge-Lenz.
- Laplace–Runge–Lenz_vector sameAs Vecteur_de_Runge-Lenz.
- Laplace–Runge–Lenz_vector sameAs Vettore_di_Lenz.
- Laplace–Runge–Lenz_vector sameAs 라플라스-룽에-렌츠_벡터.
- Laplace–Runge–Lenz_vector sameAs Laplace-Runge-Lenz-vector.
- Laplace–Runge–Lenz_vector sameAs Vetor_de_Laplace-Runge-Lenz.
- Laplace–Runge–Lenz_vector sameAs Q1153324.
- Laplace–Runge–Lenz_vector sameAs Q1153324.
- Laplace–Runge–Lenz_vector wasDerivedFrom Laplace–Runge–Lenz_vector?oldid=605770523.