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Differentiable and Complex Dynamics of Several Variables
By (author) Pei-Chu Hu, By (author) Chung-Chun Yang
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normal price: R 2 114.95
Price: R 2 008.95
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| book 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.
| product details |
Normally shipped |
Publisher | Springer
Published date | 5 Dec 2010
Language |
Format | Paperback / softback
Pages | 342
Dimensions | 235 x 155 x 0mm (L x W x H)
Weight | 0g
ISBN | 978-9-0481-5246-9
Readership Age |
BISAC | mathematics / mathematical analysis
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