Pei-Chu Hu

(Author)

Differentiable and Complex Dynamics of Several Variables (1999)Hardcover - 1999, 31 July 1999

Differentiable and Complex Dynamics of Several Variables (1999)
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Description

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.

Product Details

Book Edition:
1999
Book Format:
Hardcover
Country of Origin:
US
Date Published:
31 July 1999
Dimensions:
23.39 x 15.6 x 2.06 cm
ISBN-10:
079235771X
ISBN-13:
9780792357711
Language:
English
Location:
Dordrecht
Pages:
342
Publisher:
Weight:
680.39 gm