Solving second order ODEs using MATLAB Programming
Aim: Solve the Second order ODE using Matlab Programming and create a Animation of pendulam and its motion.
Given Problem Statement:
In given Equation
g = gravity (m/s2) = 9.81
m= mass of ball (kg) = 1
l = length of the pendulum (m) = 1
b =damping coefficient = 0.05
Simulate the motion between 0-20 sec, for angular displacement=0,angular velocity=3 rad/sec at time t=0.
solving 2nd order ODE:
Assuming theta = theta1
diffrentiate dtheta_dt = dtheta1_dt = theta2
d^2theta_dt^2 = d^2theta1_dt^2 = dtheta2_dt
d^2theta_dt^2 + (b/m)dtheta_dt +(g/l)*sin(theta) = 0
d_theta2_dt + (b/m)theta2 +(g/l)sintheta1 = 0
dtheta1_dt = theta2
dtheta2_dt = -(b/m)*theta2 - (g/l)*sin(theta1)
Software :MATLAB
Program:
clear all
close all
clc
% Input variables
% b = daming
% m = mass
% g = gravity
% l =length
b = 0.05;
g = 9.81;
l = 1;
m = 0.1;
% Intial Condition
theta_0 = [0;3];
% time points
t = linspace(0,10,100);
% solve ODE
[t,results] = ode45(@(t,theta)ode_func(t,theta,b,g,l,m),t,theta_0);
figure(1)
hold on
plot(t,results)
xlabel('time')
ylabel('theta & velocity')
legend('theta','velocity')
hold off
disp = results(:,1);
vel = results(:,2);
ct =1;
for i =1:length(disp)
x0 = 0;
y0 = 0;
x1 = l*sin(disp(i));
y1 = -l*cos(disp(i));
figure(2)
plot([x0,x1],[y0,y1],'linewidth',3,'color','b')
hold on
plot(x1,y1,'marker','o','markersize',15,'markerfacecolor','g')
axis([-1.5 1.5 -1.5 1])
plot([-1.5 1.5],[0 0],'linewidth',3)
pause(0.05)
hold off
M(ct) = getframe(gcf);
ct = ct+1;
end
movie(M)
videofile = VideoWriter('pendulum avi','uncompressed AVI')
open(videofile)
writeVideo(videofile,M)
close(videofile)
Function Code:
function [dtheta_dt] = ode_func(t,theta,b,g,l,m)
theta1 = theta(1)
theta2 = theta(2)
dtheta1_dt = theta2;
dtheta2_dt = (-b*theta2/m) - (g*sin(theta1)/l)
dtheta_dt = [dtheta1_dt; dtheta2_dt];
end
Output in Commend Window:
theta1 =
0
theta2 =
3
dtheta2_dt =
-1.5000
theta1 =
4.0190e-05
theta2 =
3.0000
dtheta2_dt =
-1.5004
theta1 =
6.0285e-05
theta2 =
3.0000
dtheta2_dt =
-1.5006
theta1 =
1.6076e-04
theta2 =
2.9999
dtheta2_dt =
-1.5015
theta1 =
1.7862e-04
theta2 =
2.9999
dtheta2_dt =
-1.5017
theta1 =
2.0095e-04
theta2 =
2.9999
dtheta2_dt =
-1.5019
theta1 =
2.0095e-04
theta2 =
2.9999
dtheta2_dt =
-1.5019
theta1 =
4.0189e-04
theta2 =
2.9998
dtheta2_dt =
-1.5038
theta1 =
5.0236e-04
theta2 =
2.9997
dtheta2_dt =
-1.5048
theta1 =
0.0010
theta2 =
2.9995
dtheta2_dt =
-1.5096
theta1 =
0.0011
theta2 =
2.9995
dtheta2_dt =
-1.5105
theta1 =
0.0012
theta2 =
2.9994
dtheta2_dt =
-1.5115
theta1 =
0.0012
theta2 =
2.9994
dtheta2_dt =
-1.5115
theta1 =
0.0022
theta2 =
2.9989
dtheta2_dt =
-1.5211
theta1 =
0.0027
theta2 =
2.9986
dtheta2_dt =
-1.5259
theta1 =
0.0052
theta2 =
2.9973
dtheta2_dt =
-1.5499
theta1 =
0.0057
theta2 =
2.9971
dtheta2_dt =
-1.5542
theta1 =
0.0062
theta2 =
2.9968
dtheta2_dt =
-1.5595
theta1 =
0.0062
theta2 =
2.9968
dtheta2_dt =
-1.5595
theta1 =
0.0112
theta2 =
2.9942
dtheta2_dt =
-1.6074
theta1 =
0.0137
theta2 =
2.9928
dtheta2_dt =
-1.6313
theta1 =
0.0263
theta2 =
2.9857
dtheta2_dt =
-1.7505
theta1 =
0.0285
theta2 =
2.9844
dtheta2_dt =
-1.7716
theta1 =
0.0313
theta2 =
2.9828
dtheta2_dt =
-1.7980
theta1 =
0.0313
theta2 =
2.9828
dtheta2_dt =
-1.7980
theta1 =
0.0562
theta2 =
2.9677
dtheta2_dt =
-2.0352
theta1 =
0.0686
theta2 =
2.9579
dtheta2_dt =
-2.1512
theta1 =
0.1298
theta2 =
2.9070
dtheta2_dt =
-2.7235
theta1 =
0.1403
theta2 =
2.8970
dtheta2_dt =
-2.8202
theta1 =
0.1538
theta2 =
2.8835
dtheta2_dt =
-2.9442
theta1 =
0.1542
theta2 =
2.8831
dtheta2_dt =
-2.9484
theta1 =
0.2604
theta2 =
2.7745
dtheta2_dt =
-3.9133
theta1 =
0.3090
theta2 =
2.6802
dtheta2_dt =
-4.3238
theta1 =
0.5209
theta2 =
2.2114
dtheta2_dt =
-5.9876
theta1 =
0.5271
theta2 =
2.1356
dtheta2_dt =
-6.0027
theta1 =
0.5708
theta2 =
1.9937
dtheta2_dt =
-6.2976
theta1 =
0.6109
theta2 =
1.9623
dtheta2_dt =
-6.6081
theta1 =
0.7117
theta2 =
1.6229
dtheta2_dt =
-7.2185
theta1 =
0.7425
theta2 =
1.4179
dtheta2_dt =
-7.3416
theta1 =
0.8424
theta2 =
0.5199
dtheta2_dt =
-7.5805
theta1 =
0.8040
theta2 =
0.4936
dtheta2_dt =
-7.3113
theta1 =
0.8074
theta2 =
0.2535
dtheta2_dt =
-7.2143
theta1 =
0.8750
theta2 =
0.0556
dtheta2_dt =
-7.5576
theta1 =
0.8783
theta2 =
-0.3895
dtheta2_dt =
-7.3556
theta1 =
0.8505
theta2 =
-0.5987
dtheta2_dt =
-7.0737
theta1 =
0.6924
theta2 =
-1.4402
dtheta2_dt =
-5.5427
theta1 =
0.6450
theta2 =
-1.3851
dtheta2_dt =
-5.2053
theta1 =
0.5789
theta2 =
-1.5648
dtheta2_dt =
-4.5843
theta1 =
0.5924
theta2 =
-1.8283
dtheta2_dt =
-4.5630
theta1 =
0.4893
theta2 =
-2.0854
dtheta2_dt =
-3.5683
theta1 =
0.4215
theta2 =
-2.1509
dtheta2_dt =
-2.9381
theta1 =
0.1275
theta2 =
-2.2754
dtheta2_dt =
-0.1094
theta1 =
0.1182
theta2 =
-2.0888
dtheta2_dt =
-0.1125
theta1 =
0.0319
theta2 =
-2.0451
dtheta2_dt =
0.7094
theta1 =
-0.0300
theta2 =
-2.3011
dtheta2_dt =
1.4448
theta1 =
-0.1550
theta2 =
-2.2226
dtheta2_dt =
2.6258
theta1 =
-0.2127
theta2 =
-2.1112
dtheta2_dt =
3.1266
theta1 =
-0.4262
theta2 =
-1.5605
dtheta2_dt =
4.8359
theta1 =
-0.3846
theta2 =
-1.4527
dtheta2_dt =
4.4068
theta1 =
-0.4320
theta2 =
-1.2546
dtheta2_dt =
4.7343
theta1 =
-0.5380
theta2 =
-1.2461
dtheta2_dt =
5.6495
theta1 =
-0.6013
theta2 =
-0.9588
dtheta2_dt =
6.0293
theta1 =
-0.6166
theta2 =
-0.7934
dtheta2_dt =
6.0693
theta1 =
-0.6549
theta2 =
-0.0779
dtheta2_dt =
6.0141
theta1 =
-0.6224
theta2 =
-0.0675
dtheta2_dt =
5.7532
theta1 =
-0.6148
theta2 =
0.1208
dtheta2_dt =
5.5980
theta1 =
-0.6608
theta2 =
0.2884
dtheta2_dt =
5.8768
theta1 =
-0.6458
theta2 =
0.5949
dtheta2_dt =
5.6064
theta1 =
-0.6203
theta2 =
0.7322
dtheta2_dt =
5.3360
theta1 =
-0.4875
theta2 =
1.2761
dtheta2_dt =
3.9573
theta1 =
-0.4587
theta2 =
1.2286
dtheta2_dt =
3.7295
theta1 =
-0.4099
theta2 =
1.3372
dtheta2_dt =
3.2408
theta1 =
-0.4092
theta2 =
1.5220
dtheta2_dt =
3.1420
theta1 =
-0.3265
theta2 =
1.6927
dtheta2_dt =
2.2997
theta1 =
-0.2747
theta2 =
1.7266
dtheta2_dt =
1.7975
theta1 =
-0.0539
theta2 =
1.7605
dtheta2_dt =
-0.3522
theta1 =
-0.0523
theta2 =
1.6223
dtheta2_dt =
-0.2988
theta1 =
0.0111
theta2 =
1.5754
dtheta2_dt =
-0.8962
theta1 =
0.0647
theta2 =
1.7512
dtheta2_dt =
-1.5094
theta1 =
0.1549
theta2 =
1.6734
dtheta2_dt =
-2.3500
theta1 =
0.1955
theta2 =
1.5858
dtheta2_dt =
-2.6984
theta1 =
0.3489
theta2 =
1.1595
dtheta2_dt =
-3.9332
theta1 =
0.3238
theta2 =
1.0894
dtheta2_dt =
-3.6661
theta1 =
0.3561
theta2 =
0.9420
dtheta2_dt =
-3.8906
theta1 =
0.4251
theta2 =
0.9170
dtheta2_dt =
-4.5040
theta1 =
0.4718
theta2 =
0.6877
dtheta2_dt =
-4.8021
theta1 =
0.4820
theta2 =
0.5559
dtheta2_dt =
-4.8252
theta1 =
0.5030
theta2 =
-0.0079
dtheta2_dt =
-4.7247
theta1 =
0.4751
theta2 =
-0.0093
dtheta2_dt =
-4.4826
theta1 =
0.4668
theta2 =
-0.1588
dtheta2_dt =
-4.3354
theta1 =
0.5041
theta2 =
-0.2993
dtheta2_dt =
-4.5887
theta1 =
0.4891
theta2 =
-0.5286
dtheta2_dt =
-4.3451
theta1 =
0.4688
theta2 =
-0.6295
dtheta2_dt =
-4.1173
theta1 =
0.3648
theta2 =
-1.0249
dtheta2_dt =
-2.9874
theta1 =
0.3442
theta2 =
-0.9836
dtheta2_dt =
-2.8184
theta1 =
0.3071
theta2 =
-1.0612
dtheta2_dt =
-2.4346
theta1 =
0.3044
theta2 =
-1.2044
dtheta2_dt =
-2.3385
theta1 =
0.2407
theta2 =
-1.3282
dtheta2_dt =
-1.6741
theta1 =
0.2014
theta2 =
-1.3506
dtheta2_dt =
-1.2871
theta1 =
0.0341
theta2 =
-1.3667
dtheta2_dt =
0.3487
theta1 =
0.0335
theta2 =
-1.2671
dtheta2_dt =
0.3049
theta1 =
-0.0139
theta2 =
-1.2300
dtheta2_dt =
0.7510
theta1 =
-0.0554
theta2 =
-1.3538
dtheta2_dt =
1.2198
theta1 =
-0.1239
theta2 =
-1.2920
dtheta2_dt =
1.8587
theta1 =
-0.1547
theta2 =
-1.2247
dtheta2_dt =
2.1239
theta1 =
-0.2718
theta2 =
-0.8967
dtheta2_dt =
3.0822
theta1 =
-0.2541
theta2 =
-0.8435
dtheta2_dt =
2.8879
theta1 =
-0.2785
theta2 =
-0.7305
dtheta2_dt =
3.0622
theta1 =
-0.3291
theta2 =
-0.7101
dtheta2_dt =
3.5259
theta1 =
-0.3651
theta2 =
-0.5317
dtheta2_dt =
3.7682
theta1 =
-0.3729
theta2 =
-0.4286
dtheta2_dt =
3.7881
theta1 =
-0.3882
theta2 =
0.0107
dtheta2_dt =
3.7082
theta1 =
-0.3659
theta2 =
0.0104
dtheta2_dt =
3.5047
theta1 =
-0.3593
theta2 =
0.1279
dtheta2_dt =
3.3858
theta1 =
-0.3891
theta2 =
0.2390
dtheta2_dt =
3.6019
theta1 =
-0.3773
theta2 =
0.4160
dtheta2_dt =
3.4066
theta1 =
-0.3617
theta2 =
0.4937
dtheta2_dt =
3.2245
theta1 =
-0.2820
theta2 =
0.7965
dtheta2_dt =
2.3314
theta1 =
-0.2663
theta2 =
0.7621
dtheta2_dt =
2.2006
theta1 =
-0.2379
theta2 =
0.8217
dtheta2_dt =
1.9007
theta1 =
-0.2358
theta2 =
0.9354
dtheta2_dt =
1.8239
theta1 =
-0.1871
theta2 =
1.0302
dtheta2_dt =
1.3100
theta1 =
-0.1573
theta2 =
1.0475
dtheta2_dt =
1.0127
theta1 =
-0.0296
theta2 =
1.0636
dtheta2_dt =
-0.2417
theta1 =
-0.0287
theta2 =
0.9906
dtheta2_dt =
-0.2138
theta1 =
0.0073
theta2 =
0.9638
dtheta2_dt =
-0.5535
theta1 =
0.0385
theta2 =
1.0550
dtheta2_dt =
-0.9055
theta1 =
0.0918
theta2 =
1.0093
dtheta2_dt =
-1.4042
theta1 =
0.1159
theta2 =
0.9581
dtheta2_dt =
-1.6133
theta1 =
0.2078
theta2 =
0.7067
dtheta2_dt =
-2.3770
theta1 =
0.1944
theta2 =
0.6646
dtheta2_dt =
-2.2273
theta1 =
0.2137
theta2 =
0.5772
dtheta2_dt =
-2.3688
theta1 =
0.2527
theta2 =
0.5633
dtheta2_dt =
-2.7345
theta1 =
0.2810
theta2 =
0.4259
dtheta2_dt =
-2.9335
theta1 =
0.2874
theta2 =
0.3460
dtheta2_dt =
-2.9537
theta1 =
0.3007
theta2 =
0.0048
dtheta2_dt =
-2.9077
theta1 =
0.2833
theta2 =
0.0044
dtheta2_dt =
-2.7440
theta1 =
0.2786
theta2 =
-0.0874
dtheta2_dt =
-2.6544
theta1 =
0.3022
theta2 =
-0.1730
dtheta2_dt =
-2.8332
theta1 =
0.2937
theta2 =
-0.3117
dtheta2_dt =
-2.6844
theta1 =
0.2819
theta2 =
-0.3729
dtheta2_dt =
-2.5422
theta1 =
0.2211
theta2 =
-0.6105
dtheta2_dt =
-1.8465
theta1 =
0.2089
theta2 =
-0.5822
dtheta2_dt =
-1.7429
theta1 =
0.1870
theta2 =
-0.6295
dtheta2_dt =
-1.5087
theta1 =
0.1858
theta2 =
-0.7208
dtheta2_dt =
-1.4521
theta1 =
0.1489
theta2 =
-0.7953
dtheta2_dt =
-1.0573
theta1 =
0.1261
theta2 =
-0.8098
dtheta2_dt =
-0.8287
theta1 =
0.0282
theta2 =
-0.8283
dtheta2_dt =
0.1378
theta1 =
0.0270
theta2 =
-0.7741
dtheta2_dt =
0.1224
theta1 =
-6.1608e-04
theta2 =
-0.7555
dtheta2_dt =
0.3838
theta1 =
-0.0240
theta2 =
-0.8245
dtheta2_dt =
0.6472
theta1 =
-0.0657
theta2 =
-0.7917
dtheta2_dt =
1.0403
theta1 =
-0.0848
theta2 =
-0.7528
dtheta2_dt =
1.2070
theta1 =
-0.1576
theta2 =
-0.5608
dtheta2_dt =
1.8201
theta1 =
-0.1472
theta2 =
-0.5268
dtheta2_dt =
1.7024
theta1 =
-0.1627
theta2 =
-0.4591
dtheta2_dt =
1.8186
theta1 =
-0.1934
theta2 =
-0.4506
dtheta2_dt =
2.1109
theta1 =
-0.2159
theta2 =
-0.3453
dtheta2_dt =
2.2741
theta1 =
-0.2212
theta2 =
-0.2835
dtheta2_dt =
2.2942
theta1 =
-0.2332
theta2 =
-0.0189
dtheta2_dt =
2.2763
theta1 =
-0.2198
theta2 =
-0.0175
dtheta2_dt =
2.1475
theta1 =
-0.2167
theta2 =
0.0541
dtheta2_dt =
2.0822
theta1 =
-0.2353
theta2 =
0.1193
dtheta2_dt =
2.2274
theta1 =
-0.2295
theta2 =
0.2285
dtheta2_dt =
2.1169
theta1 =
-0.2205
theta2 =
0.2771
dtheta2_dt =
2.0070
theta1 =
-0.1743
theta2 =
0.4653
dtheta2_dt =
1.4689
theta1 =
-0.1645
theta2 =
0.4422
dtheta2_dt =
1.3858
theta1 =
-0.1477
theta2 =
0.4803
dtheta2_dt =
1.2031
theta1 =
-0.1473
theta2 =
0.5539
dtheta2_dt =
1.1632
theta1 =
-0.1192
theta2 =
0.6129
dtheta2_dt =
0.8604
theta1 =
-0.1018
theta2 =
0.6251
dtheta2_dt =
0.6844
theta1 =
-0.0265
theta2 =
0.6449
dtheta2_dt =
-0.0622
theta1 =
-0.0252
theta2 =
0.6042
dtheta2_dt =
-0.0549
theta1 =
-0.0039
theta2 =
0.5915
dtheta2_dt =
-0.2570
theta1 =
0.0135
theta2 =
0.6445
dtheta2_dt =
-0.4546
theta1 =
0.0463
theta2 =
0.6213
dtheta2_dt =
-0.7651
theta1 =
0.0614
theta2 =
0.5919
dtheta2_dt =
-0.8982
theta1 =
0.1193
theta2 =
0.4452
dtheta2_dt =
-1.3901
theta1 =
0.1112
theta2 =
0.4178
dtheta2_dt =
-1.2970
theta1 =
0.1236
theta2 =
0.3652
dtheta2_dt =
-1.3923
theta1 =
0.1479
theta2 =
0.3606
dtheta2_dt =
-1.6263
theta1 =
0.1658
theta2 =
0.2800
dtheta2_dt =
-1.7592
theta1 =
0.1703
theta2 =
0.2323
dtheta2_dt =
-1.7783
theta1 =
0.1809
theta2 =
0.0272
dtheta2_dt =
-1.7789
theta1 =
0.1707
theta2 =
0.0252
dtheta2_dt =
-1.6787
theta1 =
0.1687
theta2 =
-0.0306
dtheta2_dt =
-1.6318
theta1 =
0.1833
theta2 =
-0.0800
dtheta2_dt =
-1.7483
theta1 =
0.1794
theta2 =
-0.1662
dtheta2_dt =
-1.6672
theta1 =
0.1726
theta2 =
-0.2047
dtheta2_dt =
-1.5827
theta1 =
0.1375
theta2 =
-0.3542
dtheta2_dt =
-1.1677
theta1 =
0.1297
theta2 =
-0.3355
dtheta2_dt =
-1.1010
theta1 =
0.1166
theta2 =
-0.3662
dtheta2_dt =
-0.9586
theta1 =
0.1169
theta2 =
-0.4253
dtheta2_dt =
-0.9313
theta1 =
0.0955
theta2 =
-0.4722
dtheta2_dt =
-0.6990
theta1 =
0.0821
theta2 =
-0.4824
dtheta2_dt =
-0.5633
theta1 =
0.0241
theta2 =
-0.5018
dtheta2_dt =
0.0143
theta1 =
0.0228
theta2 =
-0.4710
dtheta2_dt =
0.0118
theta1 =
0.0064
theta2 =
-0.4624
dtheta2_dt =
0.1685
theta1 =
-0.0067
theta2 =
-0.5034
dtheta2_dt =
0.3174
theta1 =
-0.0325
theta2 =
-0.4871
dtheta2_dt =
0.5623
theta1 =
-0.0445
theta2 =
-0.4649
dtheta2_dt =
0.6685
theta1 =
-0.0904
theta2 =
-0.3527
dtheta2_dt =
1.0617
theta1 =
-0.0840
theta2 =
-0.3306
dtheta2_dt =
0.9880
theta1 =
-0.0940
theta2 =
-0.2899
dtheta2_dt =
1.0656
theta1 =
-0.1133
theta2 =
-0.2877
dtheta2_dt =
1.2525
theta1 =
-0.1274
theta2 =
-0.2260
dtheta2_dt =
1.3598
theta1 =
-0.1311
theta2 =
-0.1891
dtheta2_dt =
1.3771
theta1 =
-0.1404
theta2 =
-0.0302
dtheta2_dt =
1.3881
theta1 =
-0.1326
theta2 =
-0.0280
dtheta2_dt =
1.3106
theta1 =
-0.1313
theta2 =
0.0154
dtheta2_dt =
1.2770
theta1 =
-0.1428
theta2 =
0.0529
dtheta2_dt =
1.3696
theta1 =
-0.1402
theta2 =
0.1207
dtheta2_dt =
1.3103
theta1 =
-0.1351
theta2 =
0.1513
dtheta2_dt =
1.2455
theta1 =
-0.1083
theta2 =
0.2698
dtheta2_dt =
0.9259
theta1 =
-0.1021
theta2 =
0.2548
dtheta2_dt =
0.8723
theta1 =
-0.0920
theta2 =
0.2795
dtheta2_dt =
0.7614
theta1 =
-0.0925
theta2 =
0.3267
dtheta2_dt =
0.7431
theta1 =
-0.0762
theta2 =
0.3639
dtheta2_dt =
0.5647
theta1 =
-0.0659
theta2 =
0.3725
dtheta2_dt =
0.4599
theta1 =
-0.0212
theta2 =
0.3902
dtheta2_dt =
0.0127
theta1 =
-0.0200
theta2 =
0.3668
dtheta2_dt =
0.0125
theta1 =
-0.0073
theta2 =
0.3610
dtheta2_dt =
-0.1090
theta1 =
0.0026
theta2 =
0.3929
dtheta2_dt =
-0.2217
theta1 =
0.0228
theta2 =
0.3814
dtheta2_dt =
-0.4147
theta1 =
0.0323
theta2 =
0.3645
dtheta2_dt =
-0.4990
theta1 =
0.0686
theta2 =
0.2787
dtheta2_dt =
-0.8119
theta1 =
0.0636
theta2 =
0.2609
dtheta2_dt =
-0.7537
theta1 =
0.0716
theta2 =
0.2293
dtheta2_dt =
-0.8164
theta1 =
0.0868
theta2 =
0.2287
dtheta2_dt =
-0.9651
theta1 =
0.0981
theta2 =
0.1813
dtheta2_dt =
-1.0511
theta1 =
0.1011
theta2 =
0.1528
dtheta2_dt =
-1.0662
theta1 =
0.1090
theta2 =
0.0297
dtheta2_dt =
-1.0819
theta1 =
0.1030
theta2 =
0.0276
dtheta2_dt =
-1.0221
theta1 =
0.1022
theta2 =
-0.0062
dtheta2_dt =
-0.9979
theta1 =
0.1112
theta2 =
-0.0347
dtheta2_dt =
-1.0711
theta1 =
0.1095
theta2 =
-0.0880
dtheta2_dt =
-1.0276
theta1 =
0.1056
theta2 =
-0.1122
dtheta2_dt =
-0.9780
theta1 =
0.0852
theta2 =
-0.2060
dtheta2_dt =
-0.7318
theta1 =
0.0802
theta2 =
-0.1940
dtheta2_dt =
-0.6890
theta1 =
0.0724
theta2 =
-0.2137
dtheta2_dt =
-0.6027
theta1 =
0.0731
theta2 =
-0.2513
dtheta2_dt =
-0.5905
theta1 =
0.0606
theta2 =
-0.2807
dtheta2_dt =
-0.4533
theta1 =
0.0526
theta2 =
-0.2877
dtheta2_dt =
-0.3724
theta1 =
0.0181
theta2 =
-0.3034
dtheta2_dt =
-0.0258
theta1 =
0.0170
theta2 =
-0.2855
dtheta2_dt =
-0.0243
theta1 =
0.0072
theta2 =
-0.2815
dtheta2_dt =
0.0701
theta1 =
-2.6096e-04
theta2 =
-0.3063
dtheta2_dt =
0.1557
theta1 =
-0.0161
theta2 =
-0.2982
dtheta2_dt =
0.3073
theta1 =
-0.0236
theta2 =
-0.2854
dtheta2_dt =
0.3741
theta1 =
-0.0522
theta2 =
-0.2195
dtheta2_dt =
0.6221
theta1 =
-0.0483
theta2 =
-0.2053
dtheta2_dt =
0.5761
theta1 =
-0.0547
theta2 =
-0.1808
dtheta2_dt =
0.6265
theta1 =
-0.0667
theta2 =
-0.1811
dtheta2_dt =
0.7444
theta1 =
-0.0756
theta2 =
-0.1446
dtheta2_dt =
0.8129
theta1 =
-0.0780
theta2 =
-0.1226
dtheta2_dt =
0.8256
theta1 =
-0.0846
theta2 =
-0.0272
dtheta2_dt =
0.8426
theta1 =
-0.0800
theta2 =
-0.0252
dtheta2_dt =
0.7964
theta1 =
-0.0795
theta2 =
0.0010
dtheta2_dt =
0.7789
theta1 =
-0.0865
theta2 =
0.0227
dtheta2_dt =
0.8365
theta1 =
-0.0854
theta2 =
0.0645
dtheta2_dt =
0.8045
theta1 =
-0.0825
theta2 =
0.0836
dtheta2_dt =
0.7664
theta1 =
-0.0669
theta2 =
0.1576
dtheta2_dt =
0.5766
theta1 =
-0.0629
theta2 =
0.1481
dtheta2_dt =
0.5425
theta1 =
-0.0568
theta2 =
0.1638
dtheta2_dt =
0.4754
theta1 =
-0.0575
theta2 =
0.1936
dtheta2_dt =
0.4675
theta1 =
-0.0548
theta2 =
0.2001
dtheta2_dt =
0.4376
theta1 =
-0.0534
theta2 =
0.2029
dtheta2_dt =
0.4219
theta1 =
-0.0461
theta2 =
0.2162
dtheta2_dt =
0.3439
theta1 =
-0.0448
theta2 =
0.2181
dtheta2_dt =
0.3308
theta1 =
-0.0431
theta2 =
0.2206
dtheta2_dt =
0.3126
theta1 =
-0.0430
theta2 =
0.2209
dtheta2_dt =
0.3110
videofile =
VideoWriter
General Properties:
Filename: 'pendulum avi.avi'
Path: 'C:UsersRehamanDesktopSkill LyncPractice Matlab'
FileFormat: 'avi'
Duration: 0
Video Properties:
ColorChannels: 3
Height: []
Width: []
FrameCount: 0
FrameRate: 30
VideoBitsPerPixel: 24
VideoFormat: 'RGB24'
VideoCompressionMethod: 'None'
Output Plot:
