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ISBN: 9789048152469

ID: 9789048152469

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. Books > Mathematics Soft cover, Springer Shop

ISBN: 9789048152469

Paperback, [PU: Springer], 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, Numerical Analysis

ISBN: 9789048152469

ID: 9789048152469

Mathematics; Global Analysis and Analysis on Manifolds; Several Complex Variables and Analytic Spaces; Partial Differential Equations; Differential Geometry; Measure and Integration analysis on manifolds, differential equation, differential geometry, dynamical systems, global analysis, integration, manifold, partial differential equation Books, Springer Shop

ISBN: 9789048152469

ID: 9789048152469

Differentiable and Complex Dynamics of Several Variables Differentiable-and-Complex-Dynamics-of-Several-Variables~~Pei-Chu-Hu Science>Mathematics>Mathematics Paperback, Springer Netherlands

ISBN: 9048152461

gebonden uitgave, ID: 13446791

Differentiable and Complex Dynamics of Several Variables ab 99.99 EURO Mathematics and Its Applications. Softcover reprint of hardcover 1st ed. 1999 Medien > Bücher