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Introduction to Dynamics

ISBN-10: 0521281490

ISBN-13: 9780521281492

Edition: 1982

Authors: I. C. Percival, Derek Richards

List price: $82.99
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Description:

Recent advances in dynamics, with wide applications throughout the sciences and engineering, have meant that a new approach to the subject is needed. Furthermore, the mathematical and scientific background of students has changed in recent years. In this book, the subject of dynamics is introduced at undergraduate level through the elementary qualitative theory of differential equations, the geometry of phrase curves and the theory of stability. Each subject, from the most elementary topic to some important discoveries of recent decades, is introduced through simple examples and illustrated with many diagrams. The text is supplemented with over a hundred exercises. The examples and exercises cover subjects as diverse as mechanics and population dynamics. The mathematical background required of the reader is an understanding of the elementary theory of differential equations and matrix arithmetic. The book will be of interest to second-year and third-year undergraduates at universities, polytechnics and technical colleges who are studying science and engineering courses. It is also suitable for graduates and research workers in such fields as plasma, atomic, particle and molecular physics, astronomy and theoretical ecology.
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Book details

List price: $82.99
Copyright year: 1982
Publisher: Cambridge University Press
Publication date: 12/2/1982
Binding: Paperback
Pages: 240
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.210
Language: English

Preface
First-order autonomous systems
Basic theory
Rotation
Natural boundaries
Examples from biology
Exercises
Linear transformations of the plane
Introduction
Area-preserving transformations
Transformations with dilation
Exercises
Second-order autonomous systems
Systems of order n
Phase flows of second-order autonomous systems
Fixed points, equilibrium and stability
Separation of variables
Classification of fixed points
Summary of classification
Determination of fixed points
Limit cycles
Exercises
Conservative Hamiltonian systems of one degree of freedom
Newtonian and Hamiltonian systems
Conservative systems
Linear conservative systems
The cubic potential
General potential
Free rotations
The vertical pendulum
Rotation, libration and periods
Area-preserving flows and Liouville's theorem
Exercises
Lagrangians
Introduction
The Legendre transformation
The Lagrangian equation of motion
Formulation
Exercises
Transformation theory
Introduction
The theory of time-independent transformations
The F[subscript 1] (Q, q) generating function
Other forms of generating function
The transformed Hamiltonian
Time-dependent transformations
Hamiltonians under time-dependent transformations
Group property and infinitesimal canonical transformations
Exercises
Angle-action variables
The simplest variables
The Hamiltonian in angle-action representation
The dependence of the angle variable upon q
Generating functions
Rotations
Exercises
Perturbation theory
Introduction
First-order perturbation theory for conservative Hamiltonian systems
Exercises
Adiabatic and rapidly oscillating conditions
Introduction
Elastic ball bouncing between two slowly moving planes
The linear oscillator with a slowly changing frequency
General adiabatic theory
Motion in a rapidly oscillating field: fast perturbations
Exercises
Linear Systems
Introduction
First-order systems
Forced linear oscillator
Propagators
Periodic conditions and linear maps
Linear area-preserving maps
Periodic forces and parametric resonance
Exercises
Chaotic motion and non-linear maps
Chaotic motion
Maps and discrete time
The logistic map
Quadratic area-preserving maps
Regular and chaotic motion of Hamiltonian systems
Exercises
Existence theorems
Integrals required for some soluble problems
Index