Mechanics of non-holonomic systems: A New Class of control systems by Sh.Kh Solt

Description: Mechanics of non-holonomic systems by Sh.Kh Soltakhanov, Mikhail Yushkov, S. Zegzhda A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Table of Contents Holonomic Systems.- Nonholonomic Systems.- Linear Transformation Of Forces.- Application Of A Tangent Space To The Study Of Constrained Motion.- The Mixed Problem Of Dynamics. New Class Of Control Problems.- Application Of The Lagrange Multipliers To The Construction Of Three New Methods For The Study Of Mechanical Systems.- Equations Of Motion In Quasicoordinates. Review 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) Long Description 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. Review Quote 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) Feature Gives deeper insight into theory and applications of Analytical Mechanics Details ISBN3642099386 Author S. Zegzhda Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Series Foundations of Engineering Mechanics Year 2010 Edition 1st ISBN-10 3642099386 ISBN-13 9783642099380 Format Paperback Publication Date 2010-10-21 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Short Title MECHANICS OF NON-HOLONOMIC SYS Language English Media Book DEWEY 620 Pages 332 Subtitle A New Class of control systems DOI 10.1007/978-3-540-85847-8 Edition Description Softcover reprint of hardcover 1st ed. 2009 Alternative 9783540858461 Audience Professional & Vocational Illustrations XXXII, 332 p. We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96237649;

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