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Ordinary Differential Equations and Mechanical Systems

  • Jan Awrejcewicz

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jan Awrejcewicz
    Pages 1-12
  3. Jan Awrejcewicz
    Pages 13-50
  4. Jan Awrejcewicz
    Pages 51-165
  5. Jan Awrejcewicz
    Pages 167-219
  6. Jan Awrejcewicz
    Pages 221-243
  7. Jan Awrejcewicz
    Pages 245-251
  8. Jan Awrejcewicz
    Pages 253-262
  9. Jan Awrejcewicz
    Pages 263-293
  10. Jan Awrejcewicz
    Pages 295-327
  11. Jan Awrejcewicz
    Pages 329-361
  12. Jan Awrejcewicz
    Pages 363-394
  13. Jan Awrejcewicz
    Pages 395-415
  14. Jan Awrejcewicz
    Pages 417-485
  15. Jan Awrejcewicz
    Pages 487-526
  16. Jan Awrejcewicz
    Pages 527-604
  17. Back Matter
    Pages 605-614

About this book

Introduction

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization, and ending on chaos and synchronization.

Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples, and engineering intuition.

The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

Keywords

Hamiltonian systems Jacobi-Levi-Civita equation Krylov method Legendre equation Peano and Cauchy-Picard theorem double Hopf bifurcation

Authors and affiliations

  • Jan Awrejcewicz
    • 1
  1. 1.Department of Automation, Biomechanics and MechatronicsŁódź University of TechnologyŁódźPoland

Bibliographic information