ssts__ln_function_singularity_plot.m

空间绳系卫星的仿真软件

% /*M-FILE Script SSTS__ln_function_singularity_plot MMM SSTSLAB */
% /*==================================================================================================
%  Simple Space Tether Simulation Laboratory Toolbox for Matlab 7.x
%
%  Copyright 2007 The SxLAB Family - Yi Chen - [e-mail]
% ====================================================================================================
%File description:
%     ln() is the Natural logarithm function , and in matlab
%     LOG    Natural logarithm.
%     LOG(X) is the natural logarithm of the elements of X.
%     Complex results are produced if X is not positive.
%      
%     this script is to show some singularities of ln()
% 
%  we take an example as following:
% y1= log( ( R.*cos(theta1)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(theta1) ))./(
% R.*cos(theta1)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(theta1) )));
%===================================================================================================
%  See Also:   SSTS__plot_position3d
%              SSTS__plot_position
%              SSTS__tether_dumbbell_replot
%===================================================================================================
%
%===================================================================================================
%Revision -
%Date        Name    Description of Change email                 Location
%30-Nov-2006 Yi Chen Initial version       [e-mail] Glasgow
%HISTORY$
%==================================================================================================*/

% SSTS__ln_function_singularity_plot Begin

%clear
home
close('all');
clear

cycle1 = 1;
cycle2 = 10;
cycle3 = 100;
cycle4 = 1000;

theta1 = 1 : 0.01 : cycle1*2*pi;
theta2 = 1 : 0.01 : cycle2*2*pi;
theta3 = 1 : 0.01 : cycle3*2*pi;
theta4 = 1 : 0.01 : cycle4*2*pi;

R =6890000;
L =1000;
   
y1= log( ( R.*cos(theta1)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(theta1) ))./( R.*cos(theta1)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(theta1) )));
y2= log( ( R.*cos(theta2)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(theta2) ))./( R.*cos(theta2)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(theta2) )));
y3= log( ( R.*cos(theta3)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(theta3) ))./( R.*cos(theta3)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(theta3) )));
y4= log( ( R.*cos(theta4)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(theta4) ))./( R.*cos(theta4)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(theta4) )));

% 2 pi
figure
hold on
grid on

plot(theta1./pi,y1);
xlabel('\theta ( \pi )');
ylabel('Ln( )');
title('0~2\pi');

% 20 pi
figure
hold on
grid on

plot(theta2./pi,y2);
xlabel('\theta ( \pi )');
ylabel('Ln( )');
title('0~20\pi');

% 200 pi
figure
hold on
grid on

plot(theta3./pi,y3);
xlabel('\theta ( \pi )');
ylabel('Ln( )');
title('0~200\pi');

% 2000 pi
figure
hold on
grid on

plot(theta4./pi,y4);
xlabel('\theta ( \pi )');
ylabel('Ln( )');
title('0~2000\pi');

% SSTS__ln_function_singularity_plot End