File:Phasenportraet mit vektorfeld.svg
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Summary
[edit]DescriptionPhasenportraet mit vektorfeld.svg |
Deutsch: Phasenporträt einer linearen DGl. 2. Ordnung |
Date | |
Source | Own work |
Author | Miessen |
Other versions |
Licensing
[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Source code for Matlab/GNU Octave
[edit]%
% Phasenportraet einer gedaempften Schwingung
% mit Vektorfeld und einer Trajektorie
%
% PT2-Glied
printf("Parameter fuer das PT2-Glied:\n");
d=0.15
%T = 1./ (2. * pi)
T = 1.
K = 1.
% Impulsantwort auf einen Dirac-Stoß
% Nach Wiki PT2-Glied
% K/( sqrt(1-d^2) ) * exp( -1. * (d / T) * t ) * sin( sqrt(1-d^2)/T * t + arctan( sqrt(1-d^2)/d ) )
% Nach Wiki linear gedämpfte Schwingung
% d = delta / omega_0
% T = 1. / omega_0
printf("Umrechnung fuer die linear gedaempfte Schwingung:\n");
delta = d / T
omega_0 = 1. / T
omega_d = sqrt(omega_0^2 - delta^2)
printf("Startwerte:\n");
x_0 = 1;
v_0 = 0;
printf("Berechnung:\n");
perioden = 6.
werte_pro_periode = 40.
periodendauer = 2.*pi/omega_0
t = 0:periodendauer/werte_pro_periode:periodendauer*perioden;
% Formel: x = e^(-1. * delta * t) * ( (v_0 + delta * x_0) / omega_d * sin(omega_d * t) + x_0 * cos(omega_d * t) );
printf("Berechne Zeitverhalten\n");
part_1 = e.^(-1. * delta .* t);
part_2 = (v_0 + delta * x_0) / omega_d .* sin(omega_d .* t);
part_3 = x_0 .* cos(omega_d .* t);
x = part_1 .* (part_2 .+ part_3);
printf("Plotter\n");
printf("Zeitdiagramm\n");
% TODO Normiert auf Schwingungen
plot(t/periodendauer, x);
title("Zeitdiagramm")
xlabel("Zeit in Perioden");
ylabel("Amplitude");
print("ausgabe/zeitdiagramm_zum_phasenportraet.svg", "-dsvg");
printf("Weiter mit beliebiger Taste\n");
pause
printf("Berechne Trajektorie\n");
printf("Trajektorie im Phasenportraet\n");
% part_1 = e.^(-1. * delta .* t);
% part_2 = (v_0 + delta * x_0) / omega_d .* sin(omega_d .* t);
% part_3 = x_0 .* cos(omega_d .* t);
part_1_ableit = -1. * delta * e.^(-1. * delta .* t);
part_2_ableit = (v_0 + delta * x_0) / omega_d .* omega_d .* cos(omega_d .* t);
part_3_ableit = x_0 .* omega_d .* -1. .* sin(omega_d .* t);
% x_ableit = v = Geschwindigkeit
x_ableit = part_1_ableit .* (part_2 .+ part_3) + part_1 .* (part_2_ableit .+ part_3_ableit);
v = x_ableit;
plot(x, v);
%[exit phasenportraet]=system(["echo '" "Phasenporträt mit Trajektorie" "'| iconv --from-code=UTF-8 --to-code=ISO-8859-15"], 1);
phasenportraet = "Phasenportraet mit Trajektorie";
title(phasenportraet)
xlabel("Amplitude (Auslenkung)");
ylabel("Ableitung (Geschwindigkeit)");
text(x_0 - 0.1, v_0, "Startpunkt ->", "HorizontalAlignment","right", "color", "blue");
text(0.2, -0.75, "<- Zeit", "color", "blue");
print("ausgabe/phasenportraet_mit_trajektorie.svg", "-dsvg");
printf("Weiter mit beliebiger Taste\n");
pause
printf("Phasenportraet als Vektorfeld\n");
[x_mesh, v_mesh] = meshgrid (-1.6:.2:+1.6);
% Vektor: v(x, v)
% v_x = v (bekannt)
% v_y = a (zu ermitteln)
a_mesh = -1. .* (2 .* delta .* v_mesh .+ omega_0 .* x_mesh);
% Randbedingungen: x_v und v_
quiver(x_mesh, v_mesh, v_mesh, a_mesh);
hold on;
plot(x, v, "r");
hold off;
% [exit phasenportraet]=system(["echo '" "Phasenporträt mit Vektorfeld" "'| iconv --from-code=UTF-8 --to-code=ISO-8859-15"], 1);
phasenportraet = "Phasenportraet mit Vektorfeld";
title(phasenportraet)
xlabel("Amplitude");
ylabel("Ableitung");
axis ([-1.5, +1.5, -1.5, +1.5 ]);
print("ausgabe/phasenportraet_mit_vektorfeld.svg", "-dsvg");
printf("Weiter mit beliebiger Taste\n");
pause
% EOF
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current | 12:40, 21 September 2013 | 512 × 384 (25 KB) | Miessen (talk | contribs) | User created page with UploadWizard |
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Short title | Gnuplot |
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Image title | Produced by GNUPLOT 4.6 patchlevel 0 |
Width | 100% |
Height | 100% |