Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
Holonomic systems. / Soltakhanov, Shervani Kh; Yushkov, Mikhail P.; Zegzhda, Sergei A.
Mechanics of non-holonomic systems: A New Class of control systems. ed. / Shervani Soltakhanov; Sergei Zegzhda; Mikhail Yushkov. 2009. p. 1-24 (Foundations in Engineering Mechanics).Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
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TY - CHAP
T1 - Holonomic systems
AU - Soltakhanov, Shervani Kh
AU - Yushkov, Mikhail P.
AU - Zegzhda, Sergei A.
N1 - Copyright: Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - In this chapter we introduce a notion of the point that represents a motion of mechanical system. To generate Lagrange's equations of the first and second kinds we make use of the approach demonstrating their unity and generality. This approach permits us to write Lagrange's equations in the form, which can be used both in the case of one material (mass) point and of arbitrary mechanical system with finite or infinite numbers of degrees of freedom. The notion of ideal holonomic constraints is considered from the different points of view. The connection of the obtained equations of motion with the D'Alembert - Lagrange principle is analyzed. The longitudinal motion of a car with acceleration is considered as an example of motion of a holonomic system with a nonretaining constraint.
AB - In this chapter we introduce a notion of the point that represents a motion of mechanical system. To generate Lagrange's equations of the first and second kinds we make use of the approach demonstrating their unity and generality. This approach permits us to write Lagrange's equations in the form, which can be used both in the case of one material (mass) point and of arbitrary mechanical system with finite or infinite numbers of degrees of freedom. The notion of ideal holonomic constraints is considered from the different points of view. The connection of the obtained equations of motion with the D'Alembert - Lagrange principle is analyzed. The longitudinal motion of a car with acceleration is considered as an example of motion of a holonomic system with a nonretaining constraint.
UR - http://www.scopus.com/inward/record.url?scp=67049100163&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-85847-8_1
DO - 10.1007/978-3-540-85847-8_1
M3 - Chapter
AN - SCOPUS:67049100163
SN - 9783540858461
T3 - Foundations in Engineering Mechanics
SP - 1
EP - 24
BT - Mechanics of non-holonomic systems
A2 - Soltakhanov, Shervani
A2 - Zegzhda, Sergei
A2 - Yushkov, Mikhail
ER -
ID: 71885084