Preface to the special issue on the tercentenary of the Laplace-Runge-Lenz vector

DOI10.1007/S10665-012-9599-0zbMath1360.00101OpenAlexW2063851085MaRDI QIDQ525135

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Publication date: 28 April 2017

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-012-9599-0

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) Collections of articles of miscellaneous specific interest (00B15) Two-body problems (70F05) Geometric theory, characteristics, transformations in context of PDEs (35A30) Proceedings, conferences, collections, etc. pertaining to ordinary differential equations (34-06) Proceedings, conferences, collections, etc. pertaining to partial differential equations (35-06)

Cites Work

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• Integrals of motion for the classical two-body problem with drag
• Conserved vectors for the autonomous system \(\ddot r+g(r,\theta)\hat r+h(r,\theta){\hat \theta}=0\)
• The harmony in the Kepler and related problems
• The first integrals and orbit equation for the Kepler problem with drag
• The relationship between the symmetries of and the existence of conserved vectors for the equation r^..+f(r)L+g(r)r=0
• The Jacobi Last Multiplier and its applications in mechanics
• Hamilton-like vectors for a class of Kepler problems with a force proportional to the velocity
• Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
• FIRST INTEGRALS ASSOCIATED WITH THE ADDITIONAL SYMMETRY OF CENTRAL FORCE PROBLEMS WITH POWER LAW POTENTIALS
• Generalisations of the LaplaceRungeLenz Vector
• A note on the construction of the Ermakov$ndash$Lewis invariant
• Jacobi's last multiplier and symmetries for the Kepler problem plus a lineal story
• The Lie Algebra sl(2, R) and so-called Kepler-Ermakov Systems
• The first integrals and their Lie algebra of the most general autonomous Hamiltonian of the form H = T + V possessing a Laplace-Runge-Lenz vector
• An analytic solution to the classical two-body problem with drag
• The Ermanno–Bernoulli constants and representations of the complete symmetry group of the Kepler problem
• Reduction of the classical MICZ-Kepler problem to a two-dimensional linear isotropic harmonic oscillator

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