ssts__tether_mmet_ii_u_energy_plot.m

空间绳系卫星的仿真软件

function [ error_status ] = SSTS__tether_MMET_II_U_energy_plot( R, L,psi,ro,A,MM,MP,N )
% /*M-FILE Function SSTS__tether_MMET_II_U_energy_plot MMM SSTSLAB */
% /*==================================================================================================
%  Simple Space Tether Simulation Laboratory Toolbox for Matlab 7.x
%
%  Copyright 2007 The SxLAB Family - Yi Chen - [e-mail]
% ====================================================================================================
%File description:
% to avoid ln( ) function's singularity at psi = pi, an alternativ
% description of the potential energy of MMET-II is derived, which
% discretises the tether mass into point masses
% 
% Input:
% MP  - mass of payload;
% MM  - mass of motor x
% R   - distance from the earth center to motor mass 
% L   - length of tether
% psi - angle of tether rotating
% ro  - density of tether
% A   - area of tether
% 
% Output:
% error_status   0 -- ok
%               !0 -- fail
%===================================================================================================
%  See Also:   SSTS__plot_position3d
%              SSTS__plot_position
%              SSTS__tether_dumbbell_replot
%              SSTS_ln_function_singularity_replot
%===================================================================================================
%
%===================================================================================================
%Revision -
%Date        Name    Description of Change email                 Location
%30-Nov-2006 Yi Chen Initial version       [e-mail] Glasgow
%HISTORY$
%==================================================================================================*/

% SSTS__tether_MMET_II_U_energy_plot Begin
error_status = 0 ;
if ( nargin == 0 )

SSTS__clear;

mu = 3.9877848*10^14;
ro = 1;
A  = 1000;
L  = 100;
psi = 0.1;
MP = 500;
MM = 100;
R = 6890000;

N = 25;

end

if( nargin ~= 8 & nargin~= 0 ) % step in default
    error_status = 1;
    error ('SSTS__tether_MMET_II_U_energy_plot() Error: Input Parameters...');
end

U_con = -mu*MP*small_funcs(R,L,psi,'+')...
    -mu*MP*small_funcs(R,L,psi,'-')...
    -mu*MM/R ...
    +mu*ro*A*ln( R, L, psi );


U_dis = zeros(1,N);
U_con = ones(1,N)*U_con;
error_data = zeros(1,N);

for idx = 1 : 1 : N
    
U_dis(idx) = -mu*MP*small_funcs( R, L, psi,'+')...
    -mu*MP*small_funcs( R, L, psi,'-')...
    -mu*MM/R...
    + mu*ro*A*L.*sum_point_mass( R , L , psi , idx );

error_data(idx) = U_dis(idx) - U_con(idx);

end

points = 1 : 1 : N;

figure(1)
grid on 
hold on
plot( points,U_con,'b.-',points,U_dis,'ro-' );
xlabel('N number of mass points');
ylabel('Potential Energy of MMET-II ');
title('Full vs. Discrete tether Potential Energy');
legend('full-tether','discrete-tether');    

figure(2)
grid on 
hold on
plot( points,error_data );
xlabel('N number of mass points');
ylabel('error in Potential Energy of MMET-II ');
title('Error of Full vs. Discrete tether Potential Energy');



% SSTS__tether_MMET_II_U_energy_plot End

function  [ out ] = small_funcs(R,L,psi,option )

if ( option == '+')

    out = ( R^2 + L^2 + 2*L*R*cos(psi) )^(-1/2);

elseif( option == '-')

    out = ( R^2 + L^2 - 2*L*R*cos(psi) )^(-1/2);

else

    out = NaN;

    error( 'check the input of big_block()');
end

%%sub func - 1
function [ ln_out ] = ln( R , L , psi )

ln_out = log( ( R.*cos(psi)- L + sqrt( R^2 + L^2 - 2*L*R.*cos(psi) ))./( R.*cos(psi)+ L + sqrt( R^2 + L^2 + 2*L*R.*cos(psi) )));



%%sub func - 2
function [ point_out ] = sum_point_mass( R , L , psi , N )

point_out = 0;

for idx = 1 : 1 : N

    single = -( (N*sqrt( R^2 + ( (2*idx-1)*L/2/N )^2 + ( (2*(2*idx-1)*R*L)/2/N)*cos(psi)))^(-1)) - ...
        (N*sqrt(R^2 + ( (2*idx-1)*L/2/N )^2 - ( (2*(2*idx-1)*R*L)/2/N)*cos(psi)))^(-1);

    point_out  = single + point_out;
    
end