Introduction to Dynamics

Name: Introduction to Dynamics
Price: 7.59 USD
Availability: InStock
ISBN: 9780521281492

ISBN-10: 0521281490

ISBN-13: 9780521281492

Edition: 1982

Authors: I. C. Percival, Derek Richards

List price: $84.99

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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…

Book details

List price: $84.99
Copyright year: 1982
Publisher: Cambridge University Press
Publication date: 12/2/1982
Binding: Paperback
Pages: 240
Size: 5.91" wide x 8.98" long x 1.02" tall
Weight: 0.748
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