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Non-Linear Differential Equations and Dynamical Systems
SPAR
kr 417
Non-Linear Differential Equations and Dynamical Systems

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
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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
Produktdetaljer
Sprog: Engelsk
Sider: 306
ISBN-13: 9780367137199
Indbinding: Hardback
Udgave:
ISBN-10: 0367137194
Udg. Dato: 13 nov 2019
Længde: 24mm
Bredde: 162mm
Højde: 240mm
Oplagsdato: 13 nov 2019
Forfatter(e) Luis Manuel (University of Lisbon Braga da Costa Campos, Luis Manuel Braga da Costa Campos


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Hardback


Sider 306


Udgave


Længde 24mm


Bredde 162mm


Højde 240mm

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