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Differentiable and Complex Dynamics of Several Variables by Pei-Chu Hu

Differentiable and Complex Dynamics of Several Variables

by Pei-Chu Hu
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Book cover type: Paperback
  • ISBN13: 9789048152469
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 342
  • Original Price: EUR 49.99
  • Language: English
  • Edition: N/A
  • Item Weight: 532 grams
  • BISAC Subject(s): Mathematical Analysis, Differential Equations / General, and Geometry / Differential

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.

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