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This article is cited in 25 scientific papers (total in 25 papers)
Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics
A. V. Borisova, I. S. Mamaevb, I. A. Bizyaevc a Udmurtian State University
b Izhevsk State Technical University
c National Research University "Higher School of Economics"
Abstract:
This is a survey of the main forms of equations of dynamical systems with non-integrable constraints, divided into two large groups. The first group contains systems arising in vakonomic mechanics and optimal control theory, with the equations of motion obtained from the variational principle, and the second contains systems in classical non-holonomic mechanics, when the constraints are ideal and therefore the D'Alembert–Lagrange principle holds.
Bibliography: 134 titles.
Keywords:
non-integrable constraints, vakonomic mechanics, optimal control theory, sub-Riemannian geometry, non-holonomic mechanics, invariant measure.
Received: 09.06.2017
Citation:
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
Linking options:
https://www.mathnet.ru/eng/rm9783https://doi.org/10.1070/RM9783 https://www.mathnet.ru/eng/rm/v72/i5/p3
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