{"product_id":"differentiable-and-complex-dynamics-of-several-variables-von-chung-chun-yang-pei-chu-hu","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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792357711\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048152469\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792357711","offer_id":50827674758,"sku":"9780792357711","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048152469","offer_id":39415568924765,"sku":"9789048152469","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/564ca669-f83f-4547-8ec8-a4f02f0f3a83.jpg?v=1772088134","url":"https:\/\/shop.autorenwelt.de\/en\/products\/differentiable-and-complex-dynamics-of-several-variables-von-chung-chun-yang-pei-chu-hu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}