File:Anharmonic oscillators solutions.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 512 × 470 pixels. Other resolutions: 261 × 240 pixels | 523 × 480 pixels | 837 × 768 pixels | 1,116 × 1,024 pixels | 2,231 × 2,048 pixels.
Original file (SVG file, nominally 512 × 470 pixels, file size: 138 KB)
File information
Structured data
Captions
Contents
Summary
[edit]DescriptionAnharmonic oscillators solutions.svg |
English: solution to several anharmonic oscillator problems |
Date | |
Source | Own work |
Author | Jkrieger |
Other versions |
Sourcecode
[edit]Note: This script need the plot2svg() function package by Juerg Schwizer!
Source code
InfoField
MATLAB code
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% three function files
function [ dy ] = harmonic( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1))/m;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [ dy ] = anharmonicA( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1)+l*y(1)^2)/m;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [ dy ] = anharmonicB( t,y,m,k,l,c )
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
dy=zeros(2,1);
dy(1)=y(2);
dy(2)=-(c*y(2)+k*y(1)+l*y(1)^3)/m;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% main script
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
addpath('plot2svg');
m=1;
k=1;
l=0.2;
c=0;
x0=0.2;
x01=2.4;
x02=0;
p02=2;
p0=0;
PSX0range=0:(0.4):(2.4);
PSRange=[-4.5 4.5];
dy=@(t,y) anharmonicA(t,y,m,k,l,c);
dyB=@(t,y) anharmonicB(t,y,m,k,l,c);
dyh=@(t,y) harmonic(t,y,m,k,l,c);
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4]);
h=figure(1);
subplot(3,2,1);
[T,Y] = ode45(dy,[0 40],[x0, p0],options);
[Th,Yh] = ode45(dyh,[0 40],[x0, p0],options);
[TB,YB] = ode45(dyB,[0 40],[x0, p0],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r-', TB,YB(:,1),'g-');
ylim([-1.5 1.5]*x0);
xlabel('Zeit t');
ylabel('Ort x(t)');
title(['\bf Trajektorie für kleine Anfangsauslenkung (x_0=' num2str(x0) ', p_0=0)']);
subplot(3,2,2);
for x0=PSX0range
[Th,Yh] = ode45(dyh,[0 10],[x0, p0],options);
plot(Yh(:,1),Yh(:,2), 'b-');
if x0==PSX0range(1)
hold on
end
end
hold off
xlim(PSRange);
ylim(PSRange);
daspect([1 1 1]);
xlabel('position x');
ylabel('impulse p');
title(['\bf Phasenraum-Plot, harmonischer Oszillator']);
subplot(3,2,3);
[T,Y] = ode45(dy,[0 40],[x01, p0],options);
[Th,Yh] = ode45(dyh,[0 40],[x01, p0],options);
[TB,YB] = ode45(dyB,[0 40],[x01, p0],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r-', TB,YB(:,1),'g-');
xlabel('Zeit t');
ylabel('Ort x(t)');
title(['\bf Trajektorie für große Anfangsauslenkung (x_0=' num2str(x01) ', p_0=0)']);
ylim([-2 2]*x01);
subplot(3,2,4);
for x0=PSX0range
[T,Y] = ode45(dy,[0 10],[x0, p0],options);
plot(Y(:,1),Y(:,2), 'r-');
if x0==PSX0range(1)
hold on
end
end
hold off
xlim(PSRange);
ylim(PSRange);
daspect([1 1 1]);
xlabel('Ort x');
ylabel('Impuls p');
title(['\bf Phasenraum-Plot, asymmetrisches Kraftgesetz']);
subplot(3,2,5);
[T,Y] = ode45(dy,[0 40],[x02, p02],options);
[Th,Yh] = ode45(dyh,[0 40],[x02, p02],options);
[TB,YB] = ode45(dyB,[0 40],[x02, p02],options);
plot(Th,Yh(:,1), 'b-', T,Y(:,1),'r-', TB,YB(:,1),'g-', [0 40], [2 2], 'b:', [0 40], -[2 2], 'b:');
xlabel('Zeit t');
ylabel('Ort x(t)');
title(['\bf Trajektorie bei gleicher Energie (x_0=' num2str(x02) ', p_0=' num2str(p02) ')' ]);
ylim([-2.5 2.5]);
subplot(3,2,6);
for x0=PSX0range
[TB,YB] = ode45(dyB,[0 10],[x0, p0],options);
plot(YB(:,1),YB(:,2), 'g-');
if x0==PSX0range(1)
hold on
end
end
hold off
xlim(PSRange);
ylim(PSRange);
daspect([1 1 1]);
xlabel('Ort x');
ylabel('Impuls p');
title(['\bf Phasenraum-Plot, symmetrisches Kraftgesetz']);
% uses the plot2svg tool from MatlabCentral by Juerg Schwizer
plot2svg('anharmonic_oscillators_solutions.svg', h)
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 05:57, 14 August 2013 | 512 × 470 (138 KB) | Jkrieger (talk | contribs) | x_0->x(0), p_0->p(0), added dashed lines | |
15:27, 1 June 2013 | 512 × 470 (153 KB) | Jkrieger (talk | contribs) | Category:Theoretical physicists Category:Created with MATLAB |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on de.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Image title | Matlab Figure Converted by PLOT2SVG written by Juerg Schwizer |
---|---|
Width | 100% |
Height | 100% |