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Dynamic Impulse Systems

Theory and Applications

  • S. T. Zavalishchin
  • A. N. Sesekin

Part of the Mathematics and Its Applications book series (MAIA, volume 394)

Table of contents

  1. Front Matter
    Pages i-xi
  2. S. T. Zavalishchin, A. N. Sesekin
    Pages 1-14
  3. S. T. Zavalishchin, A. N. Sesekin
    Pages 15-84
  4. S. T. Zavalishchin, A. N. Sesekin
    Pages 85-131
  5. S. T. Zavalishchin, A. N. Sesekin
    Pages 133-178
  6. Back Matter
    Pages 248-260

About this book

Introduction

A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco­ momics and biology, have an irregular structure: classical variational proce­ dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener­ alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat­ ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.

Keywords

construction differential equation mechanics optimization ordinary differential equation vibration

Authors and affiliations

  • S. T. Zavalishchin
    • 1
  • A. N. Sesekin
    • 1
  1. 1.Section for Nonlinear Analysis, Institute of Mathematics and MechanicsUral Department of the Russia Academy of SciencesEkatarinburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8893-5
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4790-8
  • Online ISBN 978-94-015-8893-5
  • Buy this book on publisher's site