Differentiable and Complex Dynamics of Several Variables [electronic resource] /

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.

Bibliographic Details

Main Authors:	Hu, Pei-Chu. author., Yang, Chung-Chun. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 1999
Subjects:	Mathematics., Global analysis (Mathematics)., Manifolds (Mathematics)., Measure theory., Partial differential equations., Functions of complex variables., Differential geometry., Global Analysis and Analysis on Manifolds., Several Complex Variables and Analytic Spaces., Partial Differential Equations., Differential Geometry., Measure and Integration.,
Online Access:	http://dx.doi.org/10.1007/978-94-015-9299-4
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