| 书目名称 | Differentiable and Complex Dynamics of Several Variables | | 编辑 | Pei-Chu Hu,Chung-Chun Yang | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | 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. | | 出版日期 | Book 1999 | | 关键词 | analysis on manifolds; differential equation; differential geometry; dynamical systems; global analysis; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-015-9299-4 | | isbn_softcover | 978-90-481-5246-9 | | isbn_ebook | 978-94-015-9299-4 | | copyright | Springer Science+Business Media Dordrecht 1999 |
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发表于 2025-3-21 16:39:53
