In classical mechanics, the Laplace–Runge–Lenz (LRL) vector is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical...
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Ladder operator (section Laplace–Runge–Lenz vector)
given in the literature using ladder operators, one using the Laplace–Runge–Lenz vector, another using factorization of the Hamiltonian. Another application...
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Hirzel, Leipzig, 1919) Vector Analysis (Methuen & Co., London, 1923); translated from 1919 German original by H. Levy Carl Runge und Hermann König: Vorlesungen...
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conserved quantity that corresponds to the angular momentum or to the Laplace–Runge–Lenz vector as limiting cases. The Euler three-body problem is known by a...
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Pierre-Simon, Marquis de Laplace (/ləˈplɑːs/; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French scholar whose work was important...
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standard gravitational parameter Kepler orbit Orbit Eccentricity Laplace–Runge–Lenz vector Cordani, Bruno (2003). The Kepler Problem. Birkhaeuser. p. 22...
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his application of the Laplace–Runge–Lenz vector to the old quantum mechanical treatment of hydrogen-like atoms. In 1906, Lenz graduated from the Klinger-Oberralschule...
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(Bertrand's theorem).: 92 The Kepler problem also conserves the Laplace–Runge–Lenz vector, which has since been generalized to include other interactions...
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examples include energy, linear momentum, angular momentum and the Laplace–Runge–Lenz vector (for inverse-square force laws). Constants of motion are useful...
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precession of astronomical orbits, equivalent to the rotation of the Laplace–Runge–Lenz vector. The term geodetic effect has two slightly different meanings...
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coordinate system. He appears to have been the first to show that the Laplace–Runge–Lenz vector is a constant of motion for particles acted upon by an inverse-square...
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Dipole (section Vector form)
where 2s and 2p states are "accidentally" degenerate (see article Laplace–Runge–Lenz vector for the origin of this degeneracy) and have opposite parity (2s...
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Blodgett Laplace vector – see Laplace–Runge–Lenz vector, below Laplace–Runge–Lenz vector (a.k.a. LRL vector, Laplace vector, Runge–Lenz vector, Lenz vector) –...
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disorder Laplace–Runge–Lenz vector, a vector in classical mechanics This disambiguation page lists articles associated with the title Lenz. If an internal...
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solved in multiple ways, including by demonstrating that the Laplace–Runge–Lenz vector is constant, or by applying a duality transformation to a 2-dimensional...
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centripetal force, centrifugal force, Reactive centrifugal force Laplace–Runge–Lenz vector Euler's disk elastic potential energy Mechanical equilibrium D'Alembert's...
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demon Laplace equation for irrotational flow Laplace force Laplace number Laplace plane Laplace's invariable plane Laplace pressure Laplace-Runge-Lenz vector...
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Free-fall time Gravity Kepler orbit Kepler problem Kepler's equation Laplace–Runge–Lenz vector Specific relative angular momentum, relatively easy derivation...
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approach useful in solving a variety of integral calculus problems. Laplace–Runge–Lenz vector, for an example in solving the Kepler problem "AMS Glossary of...
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dimensions [O(4)-symmetry] generated by the angular momentum and the Laplace–Runge–Lenz vector. By extending the symmetry group O(4) to the dynamical group O(4...
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studies of the celestial mechanics of astronomical bodies, is the Laplace–Runge–Lenz vector. In the late 18th and early 19th centuries, physicists developed...
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Runge–Kutta methods for numerical analysis Runge's phenomenon, a problem in the field of numerical analysis Runge's theorem Laplace–Runge–Lenz vector...
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and θ1 = θ2, then the formulae generate isoclinic rotations. Laplace–Runge–Lenz vector Lorentz group Orthogonal group Orthogonal matrix Plane of rotation...
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Foster Ramsey Jr. Carl David Tolmé Runge (1856–1927), Runge–Kutta method, Runge's phenomenon, Laplace–Runge–Lenz vector Johannes Rydberg Martin Ryle Sérgio...
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central force problem of mechanics; for further details, see the Laplace–Runge–Lenz vector article. The scale factors for the parabolic cylindrical coordinates...
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to the brachistochrone problem 1710 - Jakob Hermann shows that Laplace–Runge–Lenz vector is conserved for a case of the inverse-square central force 1714...
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of species. Lambert–Beer law was discovered by Pierre Bouguer. Laplace–Runge–Lenz vector was first discovered as a conserved quantity by Jakob Hermann...
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parallel layers with no disruption between the layers. Laplace transform Laplace–Runge–Lenz vector A vector used chiefly to describe the shape and orientation...
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problem are degenerate, corresponding to the conservation of the Laplace–Runge–Lenz vector. Degenerate motion also signals that the Hamilton–Jacobi equations...
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hyperbola. The eccentricity e is related to the total energy E (see Laplace–Runge–Lenz vector): e = 1 + 2 E L 2 k 2 m . {\displaystyle e={\sqrt {1+{\frac {2EL^{2}}{k^{2}m}}}}...
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