/usr/share/octave/site/m/sundialsTB/idas/examples_ser/midasPendI2_dns.m is in octave-sundials 2.5.0-3+b1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 | function midasPendI2_dns
%midasPendI1_dns - Simple pendulum modeled as an index-2 DAE
% The pendulum is modeled using the x and y positions with
% the constraint x^2 + y^2 = L^2
% The stabilized index-2 (GGL formulation) DAE (in first-order form)
% includes differential equations for the positions and velocities
% with additional Lagrange multipliers included in the position
% differential equations) and the position and velocity constraints.
% Radu Serban <radu@llnl.gov>
% Copyright (c) 2007, The Regents of the University of California.
% $Revision: 1.2 $Date: 2007/12/05 21:58:19 $
% x, y, vx, vy, lam, mu
neq = 6;
t0 = 0.0;
tf = 10.0;
id = ones(neq,1);
id(5) = 0;
id(6) = 0;
options = IDASetOptions('RelTol',1.e-6,...
'AbsTol',1.e-6,...
'VariableTypes',id,...
'suppressAlgVars','on',...
'MaxNumSteps', 1000,...
'LinearSolver','Dense');
y0 = zeros(neq,1);
yp0 = zeros(neq,1);
y0(1) = 1.0;
yp0(4) = 9.81;
fprintf('Consistent IC:\n');
disp([y0 yp0])
IDAInit(@pendGGL_f,t0,y0,yp0,options);
it = 1;
time(it) = t0;
sol_y(it,:) = y0';
[res, dummy1, status] = pendGGL_f(t0, y0, yp0);
pc(it) = res(5);
vc(it) = res(6);
t = t0;
t_start = clock;
while t < tf
[status,t,y] = IDASolve(tf,'OneStep');
it = it+1;
time(it) = t;
sol_y(it,:) = y';
yp=yp0;
% For verification purposes only, compute position and velocity constraint violations
% (use dummy yp = yp0)
[res, dummy1, status] = pendGGL_f(t, y, yp0);
pc(it) = res(5);
vc(it) = res(6);
end
runtime = etime(clock,t_start);
fprintf('Solver stats:\n');
disp(IDAGetStats);
fprintf('Run time: %f\n',runtime);
figure;
subplot(3,1,1)
hold on
plot(time,sol_y(:,1),'b');
plot(time,sol_y(:,2),'r');
box on
set(gca,'XLim',[t0 tf])
title('position');
legend('x','y');
subplot(3,1,2)
hold on
plot(time,sol_y(:,3),'b');
plot(time,sol_y(:,4),'r');
box on
set(gca,'XLim',[t0 tf])
title('velocity');
legend('v_x', 'v_y');
subplot(3,1,3)
hold on
plot(time,sol_y(:,5),'b');
plot(time,sol_y(:,6),'r');
box on
set(gca,'XLim',[t0 tf])
title('Lagrange multipliers');
legend('\lambda', '\mu');
figure
plotyy(time, pc, time, vc);
box on
title('position and velocity constraint violations');
figure
subplot(2,1,1)
plot(sol_y(:,1),sol_y(:,2));
axis equal
axis tight
box on
grid on
xlabel('x');
ylabel('y');
title('trajectory');
phi = atan2( sol_y(:,1) , sol_y(:,2) );
phi_d = ( sol_y(:,1).*sol_y(:,4) - sol_y(:,2).*sol_y(:,3) ) ./ ( sol_y(:,1).^2 + sol_y(:,2).^2 ) ;
subplot(2,1,2)
plot3(time,phi, phi_d);
xlabel('time');
ylabel('\phi');
zlabel('\phi^\prime');
view(-30,15);
set(gca,'XLim',[t0 tf])
grid on
box on
title('phase plot');
IDAFree;
function [res, flag, new_data] = pendGGL_f(t,yy,yp)
g = 9.81;
m = 1.0;
b = 0.3;
L = 1.0;
x = yy(1); xd = yp(1);
y = yy(2); yd = yp(2);
vx = yy(3); vxd = yp(3);
vy = yy(4); vyd = yp(4);
lam = yy(5);
mu = yy(6);
res(1) = -xd + (vx+2*x*mu);
res(2) = -yd + (vy+2*y*mu);
res(3) = -vxd + (-b*vx+2*x*lam)/m;
res(4) = -vyd + (m*g-b*vy+2*y*lam)/m;
res(5) = x^2 + y^2 - L^2;
res(6) = 2*x*vx + 2*y*vy;
flag = 0;
new_data = [];
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