Results 51 to 60 of about 11,457,962 (286)

Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits

Mathematics, 2021
The family of Numerov-type methods that effectively uses seven stages per step is considered. All the coefficients of the methods belonging to this family can be expressed analytically with respect to four free parameters.
Vladislav N. Kovalnogov, Ruslan V. Fedorov, Andrey V. Chukalin, Theodore E. Simos, Charalampos Tsitouras   +4 more
doaj   +1 more source

WKB expansion for the angular momentum and the Kepler problem: from the torus quantization to the exact one

, 1996
We calculate the WKB series for the angular momentum and the non--relativistic 3-dim Kepler problem. This is the first semiclassical treatment of the angular momentum for terms beyond the leading WKB approximation.
Robnik, Marko, Salasnich, Luca
core   +1 more source

The generalized MIC-Kepler system

, 2003
This paper deals with dynamical system that generalizes the MIC-Kepler system. It is shown that the Schr\"{o}dinger equation for this generalized MIC-Kepler system can be separated in spherical and parabolic coordinates. The spectral problem in spherical
Bellucci S., Carpio-Bernido M.V., Chrtouani L., Chrtouani L., Drăgănescu Ch.E., Gritsev V.V., Kibler M., Kibler M., Kibler M., Levon Mardoyan, Lutsenko I.V., Mardoyan L.G., Mardoyan L.G., Mardoyan L.G., Mardoyan L.G., Mladenov I., Nersessian A., Nersessian A., Nersessian A.P., Tamm I.E., Zhedanov A.S.   +20 more
core   +3 more sources

On Berkeley’s solution to the Barrovian case

Principia: An International Journal of Epistemology, 2020
At the beginning of the 18th century, Berkeley believed an anomaly pointed out by Isaac Barrow could be regarded as important evidence against the optical theories that had been established and standardized thanks to the works of Kepler and Newton.
Carlos Alberto Cardona, Juliana Gutiérrez   +1 more
doaj   +1 more source

The five-dimensional Kepler Problem as an SU(2) Gauge System: Algebraic Constraint Quantization

, 1995
Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given.
Trunk, Michael
core   +1 more source

Microfracture for full‐thickness chondral lesions of the knee in elite athletes leads to high return‐to‐play rates

Knee Surgery, Sports Traumatology, Arthroscopy, EarlyView.
Abstract Purpose Injuries to the knee are common in elite athletes and often involve damage to the articular cartilage. Given the high demands of elite sport, full‐thickness articular cartilage defects in the knee can be career‐limiting or threatening.
David J. Haslhofer, Jobe Shatrov, Mary Jones, Wahid Abdul, Arman Motesharei, Simon V. Ball, Andy Williams   +6 more
wiley   +1 more source

Lorentz Group and Oriented MICZ-Kepler Orbits

, 2011
The MICZ-Kepler orbits are the non-colliding orbits of the MICZ Kepler problems (the magnetized versions of the Kepler problem). The oriented MICZ-Kepler orbits can be parametrized by the canonical angular momentum $\mathbf L$ and the Lenz vector ...
Meng, Guowu
core   +2 more sources

Posterior cruciate ligament involvement leads to inferior outcomes in multiligament knee injuries involving the medial collateral ligament: A systematic review and meta‐analysis

Knee Surgery, Sports Traumatology, Arthroscopy, EarlyView.
Abstract Purpose Multiligament knee injuries (MLKIs) involving the medial collateral ligament (MCL) present unique challenges in surgical management and postoperative rehabilitation. This systematic review and meta‐analysis aimed to evaluate postoperative patient‐reported outcomes in patients with MCL‐involved MLKIs, with a minimum follow‐up of 2 years.
Collin Donald Roy Hunter, Judith Sternbauer, Christian Kammerlander, Johannes Grillari, Ortrun Neuper, Justin J. Ernat, Antonio Klasan   +6 more
wiley   +1 more source

Bertrand’s theorem and the double copy of relativistic field theories

Journal of High Energy Physics
Which relativistic field theories give rise to Kepler dynamics in the two-body problem? We consider a class of Hamiltonians that is the unique relativistic extension of the Kepler problem preserving its so(4) algebra, and have orbits related through time
Dijs de Neeling, Diederik Roest, Marcello Seri, Holger Waalkens   +3 more
doaj   +1 more source

Integrable Systems: In the Footprints of the Greats

Mathematics, 2023
In his 1842 lectures on dynamics C.G. Jacobi summarized difficulties with differential equations by saying that the main problem in the integration of differential equations appears in the choice of right variables.
Velimir Jurdjevic
doaj   +1 more source