Ordinary Differential Equations and Mechanical Systems

• Main Author: Awrejcewicz, Jan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Mathematical models.; Mechanics.; Ordinary Differential Equations.; Mathematical Modeling and Industrial Mathematics.; Dynamical Systems and Ergodic Theory.

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 polynomia...

Table of Contents:

• 1. Introduction
• 2. First order ODEs
• 3. Second order ODEs
• 4. Linear ODEs
• 5. Higher-order ODEs polynomial form
• 6. Systems
• 7. Theory and criteria of similarity
• 8. Model and modeling
• 9. Phase plane and phase space
• 10. Stability
• 11. Modeling via perturbation methods
• 12. Continualization and discretization
• 13. Bifurcations
• 14. Optimization of systems
• 15. Chaos and synchronization.