{"product_id":"9780792357711","title":"Mathematics and Its Applications","description":"\u003ch1\u003eMathematics and Its Applications\u003c\/h1\u003e \u003ch2\u003ePei-Chu Hu; Chung-Chun Yang\u003c\/h2\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1999-07-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792357711\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-015-9299-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 342\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46539702206604,"sku":"9780792357711","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792357711.jpg?v=1775679199","url":"https:\/\/lateknightbooks.com\/products\/9780792357711","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}