New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00369544" target="_blank" >RIV/68407700:21240/23:00369544 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21340/23:00369544

Výsledek na webu

<a href="https://doi.org/10.1140/epjp/s13360-023-04464-6" target="_blank" >https://doi.org/10.1140/epjp/s13360-023-04464-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-023-04464-6" target="_blank" >10.1140/epjp/s13360-023-04464-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Popis výsledku v původním jazyce

We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike in the case with only scalar potential, quadratic integrability with velocity dependent potentials does not imply separability in the configuration space. The leading order terms in the pairs of commuting integrals can either generalize or have no relation to the forms leading to separation in the absence of a vector potential. We call such pairs of integrals generalized, to distinguish them from the standard ones, which would correspond to separation. Here we focus on three cases of generalized non-subgroup type integrals, namely elliptic cylindrical, prolate/oblate spheroidal and circular parabolic integrals, together with one case not related to any coordinate system. We find two new integrable systems, non-separable in the configuration space, both with generalized elliptic cylindrical integrals. In the other cases, all systems found were already known and possess standard pairs of integrals. In the limit of vanishing vector potential, both systems reduce to free motion and therefore separate in every orthogonal coordinate system.

Název v anglickém jazyce

New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases

Popis výsledku anglicky

We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike in the case with only scalar potential, quadratic integrability with velocity dependent potentials does not imply separability in the configuration space. The leading order terms in the pairs of commuting integrals can either generalize or have no relation to the forms leading to separation in the absence of a vector potential. We call such pairs of integrals generalized, to distinguish them from the standard ones, which would correspond to separation. Here we focus on three cases of generalized non-subgroup type integrals, namely elliptic cylindrical, prolate/oblate spheroidal and circular parabolic integrals, together with one case not related to any coordinate system. We find two new integrable systems, non-separable in the configuration space, both with generalized elliptic cylindrical integrals. In the other cases, all systems found were already known and possess standard pairs of integrals. In the limit of vanishing vector potential, both systems reduce to free motion and therefore separate in every orthogonal coordinate system.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

EUROPEAN PHYSICAL JOURNAL PLUS

ISSN

2190-5444

e-ISSN

—

Svazek periodika

138

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

1-24

Kód UT WoS článku

001075707200010

EID výsledku v databázi Scopus

2-s2.0-85172394124