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
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Academic and Professional Practice & Development
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-1-032-65372-3 (9781032653723)
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Schweitzer Klassifikation
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.
Autor*in
University of Lisbon, Portugal
3. Differentials and First-Order Differential Equations. 4. Unsteady, Non-Linear, and Chaotic
Systems.
