By Professor Dr. Dietrich Stauffer, Professor Dr. Friedrich W. Hehl, Dipl.-Phys. Volker Winkelmann, Professor Dr. John G. Zabolitzky (auth.)
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Additional info for Computer Simulation and Computer Algebra: Lectures for Beginners
It is seen that the energy conservation is good to about 1% or better - but this is by no means good enough to provide an accurate flight path. The coordinates and velocities vary all over the place, and no definite answer can be obtained. One m u s t use double precision arithmetic to solve this problem - which we are not :intending to do. Even:in double preCision, the problem will only be pushed to somewhat larger times , it will always recur eventually. This is the a little simpler case of tmax=11.
53) '" In (53) u",(x) is the eigenfunction for frequency w. Since we know that the vibration is to be periodic in time, it is reasonable to expect that the time-dependent coefficients u(w, t) will be sin and cos; let us tryout if an ansatz like that can work. We assume that the solution u(x, t) can be written as u(x, t) = 2: u",(x)(a", sinwt + b", coswt) (54) '" and tryout this ansatz in (52). In order to do that, we have to differentiate (54), giving 82 u 8t 2 = 2: uw(x)( -w2)(a", sinwt + b", coswt), (55) '" which is rather trivial since sin and cos are differentiated easily, and u",( x) does not have any time dependence.
Eq. ) return c which bound to replace ? It. ) then b=x fb=fx else a=x fa=fx endif goto 1 end jgzY. 630176 -1. 035937 -1. 034570 -1. 334668 1. 326234 1. 053125 1. 055396 1. 239746 1. 74860e-07 O. gt. ) then write (*,*) 'bounding interval incorrect' x=O. return endif c initialize point-iterate at a x=(a+b)/2. It. gt. eq. or. eq. eq. ) return c which bound to replace ? It. 326234 1. 6 Statics and Dynamics of Strings We now turn to the configuration of a string stretched between two anchoring points, subject to a tension T, shown below.
Computer Simulation and Computer Algebra: Lectures for Beginners by Professor Dr. Dietrich Stauffer, Professor Dr. Friedrich W. Hehl, Dipl.-Phys. Volker Winkelmann, Professor Dr. John G. Zabolitzky (auth.)