{"product_id":"differentiable-and-complex-dynamics-of-pei-chu-hu-9780792357711","title":"Differentiable and Complex Dynamics of Several Variables","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Pei-Chu Hu, Chung-Chun Yang\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 079235771X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792357711\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/31\/1999\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 342\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.50lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.81d","brand":"Pei-Chu Hu","offers":[{"title":"Hardcover","offer_id":46906595442943,"sku":"9780792357711","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_8070d1e7-cdea-432d-a1a0-3609e03ecf45.jpg?v=1748770875","url":"https:\/\/www.whiterainbookhouse.com\/products\/differentiable-and-complex-dynamics-of-pei-chu-hu-9780792357711","provider":"WR Book House","version":"1.0","type":"link"}