Foundations of Engineering Mechanics

Mechanics of non-holonomic systems

A New Class of control systems

Authors: Soltakhanov, Sh.Kh, Yushkov, Mikhail, Zegzhda, S.

  • Gives deep insight into theory and applications of Analytical Mechanics

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  • ISBN 978-3-540-85847-8
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  • ISBN 978-3-540-85846-1
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Softcover $249.00
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  • ISBN 978-3-642-09938-0
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About this book

A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. The system of equations of motion in the generalized coordinates is regarded as a one vector relation, represented in a space tangential to a manifold of all possible positions of system at given instant. The tangential space is partitioned by the equations of constraints into two orthogonal subspaces. In one of them for the constraints up to the second order, the motion low is given by the equations of constraints and in the other one for ideal constraints, it is described by the vector equation without reactions of connections. In the whole space the motion low involves Lagrangian multipliers. It is shown that for the holonomic and nonholonomic constraints up to the second order, these multipliers can be found as the function of time, positions of system, and its velocities. The application of Lagrangian multipliers for holonomic systems permits us to construct a new method for determining the eigenfrequencies and eigenforms of oscillations of elastic systems and also to suggest a special form of equations for describing the system of motion of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as programming constraints such that their validity is provided due to the existence of generalized control forces, which are determined as the functions of time. The closed system of differential equations, which makes it possible to find as these control forces, as the generalized Lagrange coordinates, is compound. The theory suggested is illustrated by the examples of a spacecraft motion. The book is primarily addressed to specialists in analytic mechanics.

Reviews

From the reviews:

“‘This monograph can be useful for English scientists. It will help them to get acquainted with a rather great number of works by Russian scientists.’ … the book gives an exhaustive account of many theoretical results and applications on non-holonomic mechanics, which often had little circulation in the literature; in this respect, the historical overview of the subject, with an emphasis on the contribution by the Russian school, is interesting. … Many applications are discussed in detail using different approaches … .” (Carlo Morosi, Mathematical Reviews, Issue 2011 j)

Table of contents (7 chapters)

  • Holonomic Systems

    Soltakhanov, Shervani Kh. (et al.)

    Pages 1-24

  • Nonholonomic Systems

    Soltakhanov, Shervani Kh. (et al.)

    Pages 25-76

  • Linear Transformation Of Forces

    Soltakhanov, Shervani Kh. (et al.)

    Pages 77-104

  • Application Of A Tangent Space To The Study Of Constrained Motion

    Soltakhanov, Shervani Kh. (et al.)

    Pages 105-124

  • The Mixed Problem Of Dynamics. New Class Of Control Problems

    Soltakhanov, Shervani Kh. (et al.)

    Pages 125-148

Buy this book

eBook $189.00
price for USA (gross)
  • ISBN 978-3-540-85847-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
  • ISBN 978-3-540-85846-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
  • ISBN 978-3-642-09938-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mechanics of non-holonomic systems
Book Subtitle
A New Class of control systems
Authors
Series Title
Foundations of Engineering Mechanics
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-85847-8
DOI
10.1007/978-3-540-85847-8
Hardcover ISBN
978-3-540-85846-1
Softcover ISBN
978-3-642-09938-0
Series ISSN
1612-1384
Edition Number
1
Number of Pages
XXXII, 332
Topics