Differentiable and Complex Dynamics of Several Variables (Mathematics and Its Applications, 483)

Chung-Chun Yang,Pei-Chu Hu

ISBN 10: 079235771X / ISBN 13: 9780792357711

Published by Springer, 1999

About this Item

Connecting readers with great books since 1972. Used textbooks may not include companion materials such as access codes, etc. May have condition issues including wear and notes/highlighting. We ship orders daily and Customer Service is our top priority!

Seller Inventory # S_333331550

Bibliographic Details

• Title: Differentiable and Complex Dynamics of Several Variables (Mathematics and Its Applications, 483)
• Publisher: Springer
• Publication Date: 1999
• Language: English
• ISBN 10: 079235771X
• ISBN 13: 9780792357711
• Binding: Hardcover
• Condition: Acceptable

About this title

Synopsis

The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.