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@article{1535300,
author = {Čech, Michal and Musilová, Jana},
article_location = {Oxford},
article_number = {AUG 2019},
doi = {http://dx.doi.org/10.1016/j.ijnonlinmec.2019.03.009},
keywords = {non-linear mechanics; constrained systems; geometrical theory on fibred manifolds; Schwarzschild metric},
language = {eng},
issn = {0020-7462},
journal = {International Journal of Non-Linear Mechanics},
title = {Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting},
url = {https://www.sciencedirect.com/science/article/pii/S0020746218304220},
volume = {114},
year = {2019}
}
TY - JOUR
ID - 1535300
AU - Čech, Michal - Musilová, Jana
PY - 2019
TI - Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting
JF - International Journal of Non-Linear Mechanics
VL - 114
IS - AUG 2019
SP - 21-26
EP - 21-26
PB - Pergamon Press
SN - 00207462
KW - non-linear mechanics
KW - constrained systems
KW - geometrical theory on fibred manifolds
KW - Schwarzschild metric
UR - https://www.sciencedirect.com/science/article/pii/S0020746218304220
L2 - https://www.sciencedirect.com/science/article/pii/S0020746218304220
N2 - 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.
ER -
ČECH, Michal a Jana MUSILOVÁ. Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting. \textit{International Journal of Non-Linear Mechanics}. Oxford: Pergamon Press, 2019, roč.~114, AUG 2019, s.~21-26. ISSN~0020-7462. Dostupné z: https://dx.doi.org/10.1016/j.ijnonlinmec.2019.03.009.
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