Stability and Bifurcation Problems
The course deals with the stability theory (Parts I,II) and its connection with the bifurcation theory (Part III). Some more recent approaches to stability problems are described, for example by methods which make use of suitable one parameter families of
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Series Editors: The Reetars of CISM Sandor Kaliszky- Budapest Mahir Sayir - Zurich Wilhelm Schneider - Wien The Secretary General of CISM Giovanni Bianchi - Milan Executive Editor Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FüR MECHANICAL SCIENCES COURSES AND LECTURES - No. 387
MODERN METHODS OF ANALYTICAL MECHANICS AND THEIR APPLICATIONS
EDITED BY VALENTIN V. RUMYANTSEV AND ALEXANDER V. KARAPETYAN RUSSIAN ACADEMY OF SCIENCES
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Springer-Verlag Wien GmbH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
This volume contains 82 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1998 by Springer-Verlag Wien Originally published bySpringer-Verlag Wien New York in 1998 SPIN 10691316
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-83138-0 ISBN 978-3-7091-2520-5 (eBook) DOI 10.1007/978-3-7091-2520-5
PREFACE
The volume contains lectures given at CISM Advanced School course "Modern methods of analytical mechanics and their applications" (Udine, June
16-20, 1997).
The course aims at giving a comprehensive and up-to-date view of modern methods of analytical mechanics (general equations of analytical dynamics and problems ofthe integrability; invariant objects; the stability and bifurcations) and their applications (rigid body dynamics; celestial mechanics; multibody systems etc.). The first part (V. Y. Rumyantsev) is devoted to the theoretical aspects of analytical mechanics: the theory of Poincare-Chetayev equations and their generalizations for mechanical systems with holonomic and nonholonomic constraints including the cases of dependent variables and quazicoordinates, the theory of integration of equations of motion; generalization of the methods of Routh, Hamilton-Jacobi, Poisson, Whittaker, Suslov etc. Generalpropositions are illustrated by mechanical examples, including a rigid body with cavities, containing fluid. The second part ( C. Sima) is devoted to the effective computations in celestial mechanics and astrodynamics: Hamiltonian formalism; invariant objects (periodic orbits, invariant tori, stable and unstable manifolds, center manifolds); symbolic and numerical computations of invariant objects; applicat
