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Differentiable and Complex Dynamics of Several Variables

  • Pei-Chu Hu
  • Chung-Chun Yang

Part of the Mathematics and Its Applications book series (MAIA, volume 483)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pei-Chu Hu, Chung-Chun Yang
    Pages 1-37
  3. Pei-Chu Hu, Chung-Chun Yang
    Pages 39-62
  4. Pei-Chu Hu, Chung-Chun Yang
    Pages 63-97
  5. Pei-Chu Hu, Chung-Chun Yang
    Pages 99-136
  6. Pei-Chu Hu, Chung-Chun Yang
    Pages 137-177
  7. Pei-Chu Hu, Chung-Chun Yang
    Pages 179-202
  8. Pei-Chu Hu, Chung-Chun Yang
    Pages 203-232
  9. Pei-Chu Hu, Chung-Chun Yang
    Pages 233-274
  10. Pei-Chu Hu, Chung-Chun Yang
    Pages 275-318
  11. Back Matter
    Pages 319-341

About this book

Introduction

The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.

Keywords

analysis on manifolds differential equation differential geometry dynamical systems global analysis integration manifold partial differential equation

Authors and affiliations

  • Pei-Chu Hu
    • 1
  • Chung-Chun Yang
    • 2
  1. 1.Shandong UniversityJinanChina
  2. 2.The Hong Kong University of Science and TechnologyKowloonHong Kong

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9299-4
  • Copyright Information Springer Science+Business Media B.V. 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5246-9
  • Online ISBN 978-94-015-9299-4
  • Buy this book on publisher's site
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