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Mathematica at the IfM
The computer program Mathematica is an ideal general-purpose tool for engineers. It integrates several features into a unified, interactive environment: numerical and symbolic calculations, functional, procedural, rule-based, and graphics programming, as well as animations. By using Mathematica notebooks, the research work can easily be documented. Furthermore, the well designed programming language makes it an efficient tool for the development of programs, which nontrivially use its specific strengths: - manipulation of complicated symbolic expressions, - graphics and animation, - arbitrary precision numerical calculations. Mathematica is widely used as a general-purpose tool in the daily research work at our institute. Some more specialized packages have been developed for subjects which specifically use the above-mentioned strengths of the program. Two developments in the mid 1990ies involved the graphical postprocessing of multibody simulations and asymptotic expansions for the solutions of partial differential equations. [Top]
In[1]:= Needs["DynamitePost`"] In[2]:= ext = "e_Beispielsystem"; In[3]:= subdir = "Internal:Desktop Folder:Files:\ Computer Algebra:Mma Files:Semas:Friedl:Example"; In[4]:= body = {{{.5, .5}, {-.7, .2}, {-.7, -.2}, {.5, -.5}}};In[5]:= a = ReadData["Posvel", ext, subdir]; In[6]:= FuncPlot[a, {1, 1}]Out[6]= -Graphics- In[7]:= Picture[ext, subdir, {1}, Polygons -> body, Color -> True]Berechnung des 1. Bildes Out[7]= -Graphics- In[8]:= PrepareAnimation[ext, subdir, Polygons -> body, Info -> False, CoordinateSystems -> False, TimeInfo -> True, Color -> True] Berechnung des 1. Bildes Berechnung des 2. Bildes Berechnung des 3. Bildes Berechnung des 4. Bildes Berechnung des 5. Bildes Berechnung des 6. Bildes Berechnung des 7. Bildes Berechnung des 8. Bildes Berechnung des 9. Bildes Berechnung des 10. Bildes Berechnung des 11. Bildes Berechnung des 12. Bildes Berechnung des 13. Bildes Berechnung des 14. Bildes Berechnung des 15. Bildes Berechnung des 16. Bildes Berechnung des 17. Bildes Berechnung des 18. Bildes Berechnung des 19. Bildes Berechnung des 20. Bildes Berechnung des 21. Bildes Out[8]= {{-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-},
{{-1.73692, 1.68658}, {-1.57067, 1.85283}}, {}}In[9]:= Motion[%] Out[9]=
{-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-, -Graphics-,
-Graphics-, -Graphics-, -Graphics-}
[Top]
In[1]:= Needs["SKPackagesPerturbationPDE`"] In[2]:= equ = {eps D[sigma[x][x,y],x] +
D[tau[x,y][x,y],y] == b D[u[x][x,y,t],{t,2}],
eps D[sigma[y][x,y],y] + D[tau[x,y][x,y],x] ==
b D[u[y][x,y,t],{t,2}],
sigma[x][0,y] == 0, tau[x,y][x,g] == h};In[3]:= PolyOrderListPDE[equ,
{sigma[x][x,y], sigma[y][x,y], tau[x,y][x,y]},
eps, 2];In[4]:= IndexForm[%,
AdditionalFunctions -> {u[x][x,y,t], u[y][x,y,t]}]Out[4]//IndexForm= (0) (0) tau == b u tau == b u xy ,y x,tt xy ,x y,tt (0) (0) sigma [0,y] == 0 tau [x,g] == h x xy (0) (1) (0) (1) sigma + tau == 0 sigma + tau == 0 x ,x xy ,y y ,y xy ,x (1) (1) sigma [0,y] == 0 tau [x,g] == 0 x xy (1) (2) (1) (2) sigma + tau == 0 sigma + tau == 0 x ,x xy ,y y ,y xy ,x (2) (2) sigma [0,y] == 0 tau [x,g] == 0 x xy [Top] | |||||||||||||||||||
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