Differentiable and Complex Dynamics of Several Variables (Paperback, Softcover reprint of hardcover 1st ed. 1999)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 483
Release date:	December 2010
First published:	1999
Authors:	Pei-Chu Hu • Chung-Chun Yang
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Paperback
Pages:	342
Edition:	Softcover reprint of hardcover 1st ed. 1999
ISBN-13:	978-90-481-5246-9
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
LSN:	90-481-5246-1
Barcode:	9789048152469

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