Non-linear differential equations and dynamical systems
Campos, Luis Manuel Braga da Costa
Non-linear differential equations and dynamical systems - Boca Raton : CRC Press/Taylor & Francis Group, 2020. - xxii, 283 pages : illustrations ; 25 cm. - Mathematics and physics for science and technology .
Includes bibliographical references and index.
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.
9780367137199
Differentiable dynamical systems.
Differential equations, Nonlinear.
517.9 / CAM-N
Non-linear differential equations and dynamical systems - Boca Raton : CRC Press/Taylor & Francis Group, 2020. - xxii, 283 pages : illustrations ; 25 cm. - Mathematics and physics for science and technology .
Includes bibliographical references and index.
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.
9780367137199
Differentiable dynamical systems.
Differential equations, Nonlinear.
517.9 / CAM-N
