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@article{1094347,
author = {Czudková, Lenka and Musilová, Jana},
article_location = {Nizozemí},
article_number = {April 2013},
doi = {http://dx.doi.org/10.1016/j.ijnonlinmec.2012.11.003},
keywords = {nonholonomic mechanics; constrained systems; geometrical theory on fibred manifolds},
language = {eng},
issn = {0020-7462},
journal = {International Journal of Non-Linear Mechanics},
title = {Nonholonomic mechanics: A practical application of the geometrical theory on fibred manifolds to a planimeter motion},
volume = {50},
year = {2013}
}
TY - JOUR
ID - 1094347
AU - Czudková, Lenka - Musilová, Jana
PY - 2013
TI - Nonholonomic mechanics: A practical application of the geometrical theory on fibred manifolds to a planimeter motion
JF - International Journal of Non-Linear Mechanics
VL - 50
IS - April 2013
SP - 19-24
EP - 19-24
PB - Elsevier
SN - 00207462
KW - nonholonomic mechanics
KW - constrained systems
KW - geometrical theory on fibred manifolds
N2 - A geometrical theory of general nonholonomic mechanical systems on fibred manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was developed in 1990s by Krupkova. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. Frequently considered constraints on real physical systems are based on rolling without sliding, i.e. they are holonomic, or semiholonomic, i.e. integrable. On the other hand, there exist some practical examples of systems subjected to true (non-integrable) nonholonomic constraint conditions. In this paper we study the planimeter-a mechanism for measuring areas which belongs to mechanical systems subjected to constraint conditions containing among others a true nonholonomic one. We study the planimeter motion using the above mentioned Krupkova's approach. The results of numerical solutions of constrained equations of motion, derived within the theory, are in a good agreement with theoretical ones and thus they confirm the possibility of direct application of the theory to practical situations.
ER -
CZUDKOVÁ, Lenka and Jana MUSILOVÁ. Nonholonomic mechanics: A practical application of the geometrical theory on fibred manifolds to a planimeter motion. \textit{International Journal of Non-Linear Mechanics}. Nizozemí: Elsevier, 2013, vol.~50, April 2013, p.~19-24. ISSN~0020-7462. Available from: https://dx.doi.org/10.1016/j.ijnonlinmec.2012.11.003.
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