On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00331239" target="_blank" >RIV/68407700:21340/19:00331239 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1751-8121/ab14c2" target="_blank" >https://doi.org/10.1088/1751-8121/ab14c2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ab14c2" target="_blank" >10.1088/1751-8121/ab14c2</a>
Alternative languages
Result language
angličtina
Original language name
On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals
Original language description
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system possesses a pair of integrals of motion in involution which are (at most) quadratic in momenta and whose leading order terms, that are necessarily elements of the enveloping algebra of the Euclidean algebra, are not quadratic Casimir operators of a chain of its subalgebras. By imposing in addition that one of the integrals has the leading order term L-z(2) we can consider three such commuting pairs: circular parabolic, oblate spheroidal and prolate spheroidal. We find all possible integrable systems possessing such structure of commuting integrals and describe their Hamiltonians and their integrals.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-11805S" target="_blank" >GA17-11805S: Superintegrable systems in magnetic fields in three spatial dimensions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
1751-8121
Volume of the periodical
52
Issue of the periodical within the volume
19
Country of publishing house
GB - UNITED KINGDOM
Number of pages
25
Pages from-to
—
UT code for WoS article
000464398800001
EID of the result in the Scopus database
2-s2.0-85065054813