Further volumes of this series can be found on our homepage: springer.com Slivker, V.I. Elements, 2007 ISBN 978-3-540-44718-4 Elsoufiev, S.A. Geomechanics, 2007 ISBN 978-3-540-37052-9 Awrejcewicz, J., Krysko, V.A., Krysko, A.V. Plates and Shells, 2007 ISBN 978-3-540-37261-8 Wittbrodt, E., Adamiec-Wojcik, I., Wojciech, S. Systems, 2006 ISBN 3-540-32351-1 Aleynikov, S.M. Geotechnics, 2007 ISBN 3-540-25138-3 Skubov, D.Y., Khodzhaev, K.S. Non-Linear Electromechanics, 2007 ISBN 3-540-25139 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Mechanics of Structural Strength Analysis in Thermo-Dynamics of Dynamics of Flexible Multibody Spatial Contact Problems inThe use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, BerlinPrinted on acid-free paper 9 8 7 6 5 4 3 2 1 springer. AnnotationA general approach to the generation of equations of motion of holonomic and nonholonomic systems with the constraints of any order is proposed. The system of equations of motion in generalized coordinates is regarded as 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 law of motion is given by the equations of constraints and in another, for ideal constraints, it is described by the vector equation not involving reactions of constraints. In the whole space the law of motion involves the Lagrange 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 the Lagrange multipliers to holonomic systems permits us to construct two new methods for determining the normal frequencies and normal forms of oscillations of elastic systems and also to propose a special form of equations of motion for system of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as program constraints such that their validity is provided by the existence of generalized control forces, which are determined as the functions of time. The closed system of different...
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