Non-Linear Differential Equations and Dynamical Systems: 1st Edition (Hardback) book cover

Non-Linear Differential Equations and Dynamical Systems

1st Edition

By Luis Manuel Braga da Costa Campos

CRC Press

283 pages | 45 B/W Illus.

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Hardback: 9780367137199
pub: 2019-11-20
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Non-linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set).

The first chapter considers non-linear differential equations of first order, including variable

coefficients. A first-order differential equation is equivalent to a first-order differential in two variables.

The differentials of order higher than the first and with more than two variables are also considered.

The applications include the representation of vector fields by potentials.

The second chapter in the book starts with linear oscillators with coefficients varying with time,

including parametric resonance. It proceeds to non-linear oscillators including non-linear resonance,

amplitude jumps, and hysteresis. The non-linear restoring and friction forces also apply to

electromechanical dynamos. These are examples of dynamical systems with bifurcations that may lead

to chaotic motions.

  • Presents general first-order differential equations including non-linear like the Ricatti equation
  • Discusses differentials of the first or higher order in two or more variables
  • Includes discretization of differential equations as finite difference equations
  • Describes parametric resonance of linear time dependent oscillators specified by the Mathieu functions and other methods
  • Examines non-linear oscillations and damping of dynamical systems including bifurcations and chaotic motions

Table of Contents

3. Differentials and First-Order Differential Equations. 4. Unsteady, Non-Linear, and Chaotic


About the Author

Luis Manuel Braga da Costa Campos graduated in 1972 as a Mechanical Engineer from the Instituto

Superior Tecnico (IST) of Lisbon Technical University. His tutorials as a student (1970) were

followed by a career at the same institution (IST) through all levels: Assistant (1972), Assistant

with tenure (1974), Assistant Professor (1978), Associate Professor (1982), Chair de Applied

Mathematics and Mechanics (1985). He has been coordinator of undergraduate and post-graduate

degrees in Aerospace Engineering since their creation in 1991. He is also coordinator of the

Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and

director and founder of the Center for Aeronautical and Space Science and Technology.

About the Series

Mathematics and Physics for Science and Technology

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
MEDICAL / General