Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00109780" target="_blank" >RIV/00216224:14310/19:00109780 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0020746218304220" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0020746218304220</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijnonlinmec.2019.03.009" target="_blank" >10.1016/j.ijnonlinmec.2019.03.009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting

Popis výsledku v původním jazyce

Mechanical systems with non-holonomic constraints are often studied in technical applications. In such situations linear or affine non-holonomic constraints are usually relevant. On the other hand, there exist mechanical systems which can be naturally interpreted as non-holonomic ones with non-linear constraint. Such systems occur typically in the theory of relativity. Within physical theories they are standardly described by physical methods, not as systems subjected to non-holonomic constraints. Nevertheless, every non-holonomic system can be treated by a universal purely mathematical approach — geometrical theory on fibred manifolds with Chetaev type constraint submanifolds. For describing all aspects of a system behaviour, including all symmetries and conservation laws, it is sufficient to have the corresponding unconstrained Lagrangian and the constraint. No additional physical assumptions are needed. We demonstrate this for a typical physical system with a non-linear non-holonomic constraint — a relativistic particle moving in central field of a non-rotating star. Within the geometrical theory we obtain constraint equations of motion and their solution. Especially, we obtain equations or constraint symmetries, their solution for coordinate transformations, and corresponding conservation laws from general relations obtained on the base of this universal geometrical theory.

Název v anglickém jazyce

Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting

Popis výsledku anglicky

Mechanical systems with non-holonomic constraints are often studied in technical applications. In such situations linear or affine non-holonomic constraints are usually relevant. On the other hand, there exist mechanical systems which can be naturally interpreted as non-holonomic ones with non-linear constraint. Such systems occur typically in the theory of relativity. Within physical theories they are standardly described by physical methods, not as systems subjected to non-holonomic constraints. Nevertheless, every non-holonomic system can be treated by a universal purely mathematical approach — geometrical theory on fibred manifolds with Chetaev type constraint submanifolds. For describing all aspects of a system behaviour, including all symmetries and conservation laws, it is sufficient to have the corresponding unconstrained Lagrangian and the constraint. No additional physical assumptions are needed. We demonstrate this for a typical physical system with a non-linear non-holonomic constraint — a relativistic particle moving in central field of a non-rotating star. Within the geometrical theory we obtain constraint equations of motion and their solution. Especially, we obtain equations or constraint symmetries, their solution for coordinate transformations, and corresponding conservation laws from general relations obtained on the base of this universal geometrical theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

International Journal of Non-Linear Mechanics

ISSN

0020-7462

e-ISSN

1878-5638

Svazek periodika

114

Číslo periodika v rámci svazku

AUG 2019

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

6

Strana od-do

21-26

Kód UT WoS článku

000469904900003

EID výsledku v databázi Scopus

2-s2.0-85064715563