Non-Linear Differential Equations and Dynamical Systems

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Luis Manuel Braga da Costa Campos (Instituto Superior Technico, Lisboa, Portugal)

Non-Linear Differential Equations and Dynamical Systems

Luis Manuel Braga da Costa Campos (Instituto Superior Technico, Lisboa, Portugal)

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English

CRC Press
13 November 2019

Discrete mathematics; Algebra; Differential calculus & equations; Applied mathematics; Environmental science, engineering & technology

Series: Mathematics and Physics for Science and Technology

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

By: Luis Manuel Braga da Costa Campos (Instituto Superior Technico Lisboa Portugal)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 408g
ISBN: 9780367137199
ISBN 10: 0367137194
Series: Mathematics and Physics for Science and Technology
Pages: 306
Publication Date: 13 November 2019
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

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.