By Luigi Bianchi

Questo secondo quantity riproduce in parte teorie speciali già svolte nella prima edizione del libro, che in questa costituivano i Capitoli da XI a XX, ed altre nuove ne accoglie.

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Extra resources for Lezione di geometria differenziale

Example text

1 Streamlines by analytical integration. Consider a steady two-dimensional flow with velocity components Ux = ax+ by, uy = bx-ay. 4). 2 Point particle motion in polar coordinates. 2, the position of a point particle is described by the functions x = X(t), a = £(£), and (p = <&(t). 3, the position of a point particle is described by the functions r = R(t), O = @(t), and (p = &(t). 1 Streamlines by numerical integration. Directory 04-various/strmll of FDLIB includes the main program strmll that generates streamlines emanating from a specified collection of points in the domain of a two-dimensional flow, computed by the explicit modified Euler method.

26) The corresponding relations for the components of the velocity are vr — cos 9 vx + sin 6 cos

Unless At is sufficiently small, this level of error is not tolerated in scientific computing. 3 Explicit modified Euler method To reduce the magnitude of the error, we implement a simple modification of the explicit Euler method. The new algorithm involves the following steps: 1. Set the initial time; for example, set t — O. 2. Select the size of the time step At. 3. Specify the initial coordinates X(Q), Y(O), and Z(O). 4. 7), and save them for future use. 5. 7) to obtain the predicted coordinates of the point particle at time t + At, denoted by Xpred, YPred, and ZPred.