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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Name of the periodical

International Journal of Non-Linear Mechanics

ISSN

0020-7462

e-ISSN

1878-5638

Volume of the periodical

114

Issue of the periodical within the volume

AUG 2019

Country of publishing house

GB - UNITED KINGDOM

Number of pages

6

Pages from-to

21-26

UT code for WoS article

000469904900003

EID of the result in the Scopus database

2-s2.0-85064715563