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Application of a tangent space to the study of constrained motion. / 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. 105-124 (Foundations in Engineering Mechanics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Soltakhanov, SK, Yushkov, MP & Zegzhda, SA 2009, Application of a tangent space to the study of constrained motion. in S Soltakhanov, S Zegzhda & M Yushkov (eds), Mechanics of non-holonomic systems: A New Class of control systems. Foundations in Engineering Mechanics, pp. 105-124. https://doi.org/10.1007/978-3-540-85847-8_4

APA

Soltakhanov, S. K., Yushkov, M. P., & Zegzhda, S. A. (2009). Application of a tangent space to the study of constrained motion. In S. Soltakhanov, S. Zegzhda, & M. Yushkov (Eds.), Mechanics of non-holonomic systems: A New Class of control systems (pp. 105-124). (Foundations in Engineering Mechanics). https://doi.org/10.1007/978-3-540-85847-8_4

Vancouver

Soltakhanov SK, Yushkov MP, Zegzhda SA. Application of a tangent space to the study of constrained motion. In Soltakhanov S, Zegzhda S, Yushkov M, editors, Mechanics of non-holonomic systems: A New Class of control systems. 2009. p. 105-124. (Foundations in Engineering Mechanics). https://doi.org/10.1007/978-3-540-85847-8_4

Author

Soltakhanov, Shervani Kh ; Yushkov, Mikhail P. ; Zegzhda, Sergei A. / Application of a tangent space to the study of constrained motion. Mechanics of non-holonomic systems: A New Class of control systems. editor / Shervani Soltakhanov ; Sergei Zegzhda ; Mikhail Yushkov. 2009. pp. 105-124 (Foundations in Engineering Mechanics).

BibTeX

@inbook{ebb407516a98441d8d3a07f6b77a5df1,
title = "Application of a tangent space to the study of constrained motion",
abstract = "By means of a tangent space we introduce, a system of Lagrange's equations of the second kind is represented in the vector form. It is shown that the tangential space is partitioned by equations of constraints into the direct sum of two subspaces. In one of them the component of an acceleration vector of system is uniquely determined by the equations of constraints. The notion of ideality of holonomic constraints and nonholonomic constraints of the first and second orders is analyzed. This notion is extended to high-order constraints. The relationship and equivalence of differential variational principles of mechanics are considered. A geometric interpretation of the ideality of constraints is given. Generalized Gaussian principle is formulated. By means of this principle for nonholonomic systems with third-order constraints the equations in Maggi's form and in Appell's form are obtained.",
author = "Soltakhanov, {Shervani Kh} and Yushkov, {Mikhail P.} and Zegzhda, {Sergei A.}",
note = "Copyright: Copyright 2009 Elsevier B.V., All rights reserved.",
year = "2009",
doi = "10.1007/978-3-540-85847-8_4",
language = "English",
isbn = "9783540858461",
series = "Foundations in Engineering Mechanics",
pages = "105--124",
editor = "Shervani Soltakhanov and Sergei Zegzhda and Mikhail Yushkov",
booktitle = "Mechanics of non-holonomic systems",

}

RIS

TY - CHAP

T1 - Application of a tangent space to the study of constrained motion

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 - By means of a tangent space we introduce, a system of Lagrange's equations of the second kind is represented in the vector form. It is shown that the tangential space is partitioned by equations of constraints into the direct sum of two subspaces. In one of them the component of an acceleration vector of system is uniquely determined by the equations of constraints. The notion of ideality of holonomic constraints and nonholonomic constraints of the first and second orders is analyzed. This notion is extended to high-order constraints. The relationship and equivalence of differential variational principles of mechanics are considered. A geometric interpretation of the ideality of constraints is given. Generalized Gaussian principle is formulated. By means of this principle for nonholonomic systems with third-order constraints the equations in Maggi's form and in Appell's form are obtained.

AB - By means of a tangent space we introduce, a system of Lagrange's equations of the second kind is represented in the vector form. It is shown that the tangential space is partitioned by equations of constraints into the direct sum of two subspaces. In one of them the component of an acceleration vector of system is uniquely determined by the equations of constraints. The notion of ideality of holonomic constraints and nonholonomic constraints of the first and second orders is analyzed. This notion is extended to high-order constraints. The relationship and equivalence of differential variational principles of mechanics are considered. A geometric interpretation of the ideality of constraints is given. Generalized Gaussian principle is formulated. By means of this principle for nonholonomic systems with third-order constraints the equations in Maggi's form and in Appell's form are obtained.

UR - http://www.scopus.com/inward/record.url?scp=67049134081&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85847-8_4

DO - 10.1007/978-3-540-85847-8_4

M3 - Chapter

AN - SCOPUS:67049134081

SN - 9783540858461

T3 - Foundations in Engineering Mechanics

SP - 105

EP - 124

BT - Mechanics of non-holonomic systems

A2 - Soltakhanov, Shervani

A2 - Zegzhda, Sergei

A2 - Yushkov, Mikhail

ER -

ID: 71884354