Week 3 - Solving second order ODEs
clear all
close all
clc
%inputs
%g = gravity in m/s2,
%L = length of the pendulum in m,
%m = mass of the ball in kg,
%b= damping coefficient.
L=1;
m=1;
b=0.05;
g=9.81;
%Primary conditions
x = [0 3];
% points
t = linspace( 0, 20 , 50);
%Solution ODE
[t , x] = ode45(@(t,theta) odef(t,theta,b,g,L,m),t,x); (Solving differential equation using ode 45 which is in built function)
%%
% Plot Angular displacement and Angular velocity
subplot(2,1,1)
plot (t,x(:,1) ,"LineWidth",3,"Color",'r')
plot (t,x(:,2) , "LineWidth",2,"Color",'y')
xlabel('Time (sec)')
ylabel('Angular displacement')
title( 'Pendulum Motion')
subplot(2,1,2)
plot (t, x(:,1) , "LineWidth",3,"Color",'r')
hold on
plot (t, x(:,2) , "LineWidth",2,"Color",'y')
xlabel('Time (sec)')
ylabel('Angular velocity')
title( 'Pendulum Motion')
grid on;
%ANIMATION
X0 = 0;
Y0 = 0;
ct=1; (Counter represents each and every frame)
for i= 1:length(t);
X1 = L*sin(x(i,1));
Y1 = -L*cos(x(i,1));
figure
plot([-1,1],[0,0], 'linewidth', 4, 'color' ,'g');
axis ([-2 2 -2 2]);
line ([X0 X1], [Y0 Y1] , 'linewidth', 2 , 'color' ,'b');
hold on (Retains plots in the current axes)
plot (X0 , Y0 , 'O' , 'markersize' , 3 , 'markerfacecolor','y');
plot (X1 , Y1 , 'O' , 'markersize' , 20 , 'markerfacecolor','r');
title ('Pendulum Motion');
legend ('Rod', 'Pendulum Length', 'Fixed Point' , 'Pendulum ball')
grid on;
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
function [dtheta_dt]= odef(t,theta,b,g,L,m)
theta1 = theta(1)
theta2 = theta (2)
dtheta1_dt = theta2;
dtheta2_dt = -(b/m)*theta2 - (g/L)*sin(theta1);
dtheta_dt = [ dtheta1_dt ; dtheta2_dt];
end
Command window
theta1 =
0
theta2 =
3
theta1 =
4.0190e-05
theta2 =
3.0000
theta1 =
6.0285e-05
theta2 =
3.0000
theta1 =
1.6076e-04
theta2 =
3.0000
theta1 =
1.7862e-04
theta2 =
3.0000
theta1 =
2.0095e-04
theta2 =
3.0000
theta1 =
2.0095e-04
theta2 =
3.0000
theta1 =
4.0190e-04
theta2 =
3.0000
theta1 =
5.0238e-04
theta2 =
3.0000
theta1 =
0.0010
theta2 =
2.9999
theta1 =
0.0011
theta2 =
2.9999
theta1 =
0.0012
theta2 =
2.9999
theta1 =
0.0012
theta2 =
2.9999
theta1 =
0.0022
theta2 =
2.9999
theta1 =
0.0027
theta2 =
2.9999
theta1 =
0.0052
theta2 =
2.9997
theta1 =
0.0057
theta2 =
2.9997
theta1 =
0.0062
theta2 =
2.9996
theta1 =
0.0062
theta2 =
2.9996
theta1 =
0.0113
theta2 =
2.9993
theta1 =
0.0138
theta2 =
2.9990
theta1 =
0.0263
theta2 =
2.9976
theta1 =
0.0285
theta2 =
2.9972
theta1 =
0.0313
theta2 =
2.9968
theta1 =
0.0313
theta2 =
2.9968
theta1 =
0.0564
theta2 =
2.9930
theta1 =
0.0689
theta2 =
2.9888
theta1 =
0.1311
theta2 =
2.9651
theta1 =
0.1418
theta2 =
2.9596
theta1 =
0.1556
theta2 =
2.9521
theta1 =
0.1560
theta2 =
2.9521
theta1 =
0.2635
theta2 =
2.8913
theta1 =
0.3147
theta2 =
2.8187
theta1 =
0.5410
theta2 =
2.4325
theta1 =
0.5512
theta2 =
2.3436
theta1 =
0.6003
theta2 =
2.2198
theta1 =
0.6391
theta2 =
2.2251
theta1 =
0.7529
theta2 =
1.9202
theta1 =
0.7923
theta2 =
1.7194
theta1 =
0.9255
theta2 =
0.8017
theta1 =
0.8845
theta2 =
0.7247
theta1 =
0.8987
theta2 =
0.4721
theta1 =
0.9780
theta2 =
0.3338
theta1 =
1.0001
theta2 =
-0.2068
theta1 =
0.9708
theta2 =
-0.4840
theta1 =
0.7716
theta2 =
-1.6199
theta1 =
0.6797
theta2 =
-1.5874
theta1 =
0.5958
theta2 =
-1.8621
theta1 =
0.6551
theta2 =
-2.1583
theta1 =
0.5281
theta2 =
-2.5038
theta1 =
0.4417
theta2 =
-2.6069
theta1 =
0.0571
theta2 =
-2.8053
theta1 =
0.0280
theta2 =
-2.5264
theta1 =
-0.0856
theta2 =
-2.4938
theta1 =
-0.1414
theta2 =
-2.8822
theta1 =
-0.3017
theta2 =
-2.7973
theta1 =
-0.3765
theta2 =
-2.6593
theta1 =
-0.6502
theta2 =
-1.9408
theta1 =
-0.5947
theta2 =
-1.7513
theta1 =
-0.6578
theta2 =
-1.5069
theta1 =
-0.7958
theta2 =
-1.5632
theta1 =
-0.8816
theta2 =
-1.1741
theta1 =
-0.9005
theta2 =
-0.9460
theta1 =
-0.9355
theta2 =
0.0690
theta1 =
-0.8819
theta2 =
0.1205
theta1 =
-0.8667
theta2 =
0.3884
theta1 =
-0.9359
theta2 =
0.5769
theta1 =
-0.9024
theta2 =
1.0337
theta1 =
-0.8559
theta2 =
1.2477
theta1 =
-0.6047
theta2 =
2.1040
theta1 =
-0.5411
theta2 =
2.0626
theta1 =
-0.4554
theta2 =
2.2375
theta1 =
-0.4683
theta2 =
2.4737
theta1 =
-0.3206
theta2 =
2.7307
theta1 =
-0.2295
theta2 =
2.7686
theta1 =
0.1490
theta2 =
2.6586
theta1 =
0.1471
theta2 =
2.3146
theta1 =
0.2572
theta2 =
2.2015
theta1 =
0.3503
theta2 =
2.6103
theta1 =
0.4830
theta2 =
2.4325
theta1 =
0.5392
theta2 =
2.2760
theta1 =
0.7478
theta2 =
1.5249
theta1 =
0.7099
theta2 =
1.4115
theta1 =
0.7499
theta2 =
1.1824
theta1 =
0.8468
theta2 =
1.1293
theta1 =
0.9126
theta2 =
0.6982
theta1 =
0.9172
theta2 =
0.4571
theta1 =
0.8826
theta2 =
-0.5912
theta1 =
0.8179
theta2 =
-0.6186
theta1 =
0.7826
theta2 =
-0.8908
theta1 =
0.8486
theta2 =
-1.1119
theta1 =
0.7903
theta2 =
-1.4953
theta1 =
0.7385
theta2 =
-1.6628
theta1 =
0.4769
theta2 =
-2.3145
theta1 =
0.4277
theta2 =
-2.2621
theta1 =
0.3464
theta2 =
-2.3782
theta1 =
0.3403
theta2 =
-2.5803
theta1 =
0.1876
theta2 =
-2.7664
theta1 =
0.0989
theta2 =
-2.7627
theta1 =
-0.2568
theta2 =
-2.4953
theta1 =
-0.2372
theta2 =
-2.1631
theta1 =
-0.3382
theta2 =
-2.0132
theta1 =
-0.4489
theta2 =
-2.3717
theta1 =
-0.5657
theta2 =
-2.1563
theta1 =
-0.6121
theta2 =
-1.9937
theta1 =
-0.7831
theta2 =
-1.2287
theta1 =
-0.7506
theta2 =
-1.1362
theta1 =
-0.7794
theta2 =
-0.9137
theta1 =
-0.8588
theta2 =
-0.8318
theta1 =
-0.9089
theta2 =
-0.3818
theta1 =
-0.9035
theta2 =
-0.1372
theta1 =
-0.8214
theta2 =
0.9042
theta1 =
-0.7502
theta2 =
0.9090
theta1 =
-0.7019
theta2 =
1.1758
theta1 =
-0.7648
theta2 =
1.4191
theta1 =
-0.6879
theta2 =
1.7833
theta1 =
-0.6272
theta2 =
1.9299
theta1 =
-0.3336
theta2 =
2.4433
theta1 =
-0.2885
theta2 =
2.3310
theta1 =
-0.1996
theta2 =
2.4042
theta1 =
-0.1823
theta2 =
2.6501
theta1 =
-0.0283
theta2 =
2.7457
theta1 =
0.0549
theta2 =
2.6951
theta1 =
0.3764
theta2 =
2.2699
theta1 =
0.3406
theta2 =
1.9819
theta1 =
0.4276
theta2 =
1.7977
theta1 =
0.5516
theta2 =
2.0604
theta1 =
0.6560
theta2 =
1.7949
theta1 =
0.6930
theta2 =
1.6149
theta1 =
0.8189
theta2 =
0.7883
theta1 =
0.7806
theta2 =
0.7134
theta1 =
0.7955
theta2 =
0.4809
theta1 =
0.8705
theta2 =
0.3634
theta1 =
0.8932
theta2 =
-0.1068
theta1 =
0.8715
theta2 =
-0.3502
theta1 =
0.7169
theta2 =
-1.3467
theta1 =
0.6401
theta2 =
-1.3115
theta1 =
0.5728
theta2 =
-1.5566
theta1 =
0.6260
theta2 =
-1.8317
theta1 =
0.5228
theta2 =
-2.1503
theta1 =
0.4510
theta2 =
-2.2548
theta1 =
0.1246
theta2 =
-2.5212
theta1 =
0.0940
theta2 =
-2.3178
theta1 =
-0.0024
theta2 =
-2.3181
theta1 =
-0.0436
theta2 =
-2.6259
theta1 =
-0.1910
theta2 =
-2.5946
theta1 =
-0.2627
theta2 =
-2.4884
theta1 =
-0.5288
theta2 =
-1.8933
theta1 =
-0.4814
theta2 =
-1.6908
theta1 =
-0.5460
theta2 =
-1.4756
theta1 =
-0.6717
theta2 =
-1.5818
theta1 =
-0.7556
theta2 =
-1.2540
theta1 =
-0.7779
theta2 =
-1.0541
theta1 =
-0.8341
theta2 =
-0.1597
theta1 =
-0.7874
theta2 =
-0.1079
theta1 =
-0.7816
theta2 =
0.1341
theta1 =
-0.8491
theta2 =
0.2938
theta1 =
-0.8317
theta2 =
0.7292
theta1 =
-0.7940
theta2 =
0.9378
theta1 =
-0.5827
theta2 =
1.7636
theta1 =
-0.5199
theta2 =
1.7054
theta1 =
-0.4435
theta2 =
1.8859
theta1 =
-0.4660
theta2 =
2.1432
theta1 =
-0.3428
theta2 =
2.3905
theta1 =
-0.2651
theta2 =
2.4415
theta1 =
0.0665
theta2 =
2.4446
theta1 =
0.0745
theta2 =
2.1804
theta1 =
0.1704
theta2 =
2.1089
theta1 =
0.2404
theta2 =
2.4385
theta1 =
0.3685
theta2 =
2.3094
theta1 =
0.4249
theta2 =
2.1744
theta1 =
0.6328
theta2 =
1.5074
theta1 =
0.5928
theta2 =
1.3813
theta1 =
0.6358
theta2 =
1.1663
theta1 =
0.7363
theta2 =
1.1523
theta1 =
0.8003
theta2 =
0.7830
theta1 =
0.8092
theta2 =
0.5713
theta1 =
0.8015
theta2 =
-0.3529
theta1 =
0.7465
theta2 =
-0.3813
theta1 =
0.7226
theta2 =
-0.6252
theta1 =
0.7843
theta2 =
-0.8172
theta1 =
0.7410
theta2 =
-1.1821
theta1 =
0.6976
theta2 =
-1.3452
theta1 =
0.4748
theta2 =
-1.9829
theta1 =
0.4288
theta2 =
-1.9302
theta1 =
0.3568
theta2 =
-2.0526
theta1 =
0.3562
theta2 =
-2.2568
theta1 =
0.2263
theta2 =
-2.4473
theta1 =
0.1490
theta2 =
-2.4629
theta1 =
-0.1697
theta2 =
-2.3184
theta1 =
-0.1630
theta2 =
-2.0478
theta1 =
-0.2533
theta2 =
-1.9393
theta1 =
-0.3391
theta2 =
-2.2446
theta1 =
-0.4477
theta2 =
-2.0812
theta1 =
-0.4931
theta2 =
-1.9464
theta1 =
-0.6647
theta2 =
-1.2972
theta1 =
-0.6382
theta2 =
-1.2020
theta1 =
-0.6701
theta2 =
-1.0062
theta1 =
-0.7427
theta2 =
-0.9572
theta1 =
-0.7973
theta2 =
-0.5759
theta1 =
-0.8001
theta2 =
-0.3618
theta1 =
-0.7633
theta2 =
0.5582
theta1 =
-0.7040
theta2 =
0.5709
theta1 =
-0.6719
theta2 =
0.8121
theta1 =
-0.7324
theta2 =
1.0208
theta1 =
-0.6803
theta2 =
1.3532
theta1 =
-0.6351
theta2 =
1.4961
theta1 =
-0.4092
theta2 =
2.0441
theta1 =
-0.3687
theta2 =
1.9854
theta1 =
-0.2984
theta2 =
2.0830
theta1 =
-0.2909
theta2 =
2.2735
theta1 =
-0.1606
theta2 =
2.4283
theta1 =
-0.0854
theta2 =
2.4249
theta1 =
0.2191
theta2 =
2.2110
theta1 =
0.2053
theta2 =
1.9507
theta1 =
0.2903
theta2 =
1.8265
theta1 =
0.3818
theta2 =
2.1025
theta1 =
0.4841
theta2 =
1.9195
theta1 =
0.5253
theta2 =
1.7786
theta1 =
0.6771
theta2 =
1.1100
theta1 =
0.6490
theta2 =
1.0234
theta1 =
0.6751
theta2 =
0.8257
theta1 =
0.7447
theta2 =
0.7616
theta1 =
0.7888
theta2 =
0.3743
theta1 =
0.7857
theta2 =
0.1616
theta1 =
0.7221
theta2 =
-0.7390
theta1 =
0.6610
theta2 =
-0.7370
theta1 =
0.6220
theta2 =
-0.9703
theta1 =
0.6785
theta2 =
-1.1903
theta1 =
0.6164
theta2 =
-1.5087
theta1 =
0.5666
theta2 =
-1.6384
theta1 =
0.3243
theta2 =
-2.1050
theta1 =
0.2865
theta2 =
-2.0154
theta1 =
0.2125
theta2 =
-2.0884
theta1 =
0.1985
theta2 =
-2.2992
theta1 =
0.0675
theta2 =
-2.4028
theta1 =
-0.0046
theta2 =
-2.3728
theta1 =
-0.2897
theta2 =
-2.0641
theta1 =
-0.2666
theta2 =
-1.8227
theta1 =
-0.3439
theta2 =
-1.6771
theta1 =
-0.4426
theta2 =
-1.9060
theta1 =
-0.5374
theta2 =
-1.6925
theta1 =
-0.5728
theta2 =
-1.5405
theta1 =
-0.6967
theta2 =
-0.8336
theta1 =
-0.6642
theta2 =
-0.7586
theta1 =
-0.6819
theta2 =
-0.5543
theta1 =
-0.7498
theta2 =
-0.4672
theta1 =
-0.7775
theta2 =
-0.0703
theta1 =
-0.7649
theta2 =
0.1399
theta1 =
-0.6602
theta2 =
1.0071
theta1 =
-0.5969
theta2 =
0.9805
theta1 =
-0.5473
theta2 =
1.1994
theta1 =
-0.5969
theta2 =
1.4388
theta1 =
-0.5197
theta2 =
1.7311
theta1 =
-0.4634
theta2 =
1.8375
theta1 =
-0.2002
theta2 =
2.1695
theta1 =
-0.1690
theta2 =
2.0339
theta1 =
-0.0904
theta2 =
2.0669
theta1 =
-0.0642
theta2 =
2.3054
theta1 =
0.0656
theta2 =
2.3344
theta1 =
0.1323
theta2 =
2.2682
theta1 =
0.3872
theta2 =
1.8367
theta1 =
0.3535
theta2 =
1.6314
theta1 =
0.4188
theta2 =
1.4595
theta1 =
0.5240
theta2 =
1.6111
theta1 =
0.6064
theta2 =
1.3558
theta1 =
0.6329
theta2 =
1.1895
theta1 =
0.7141
theta2 =
0.4351
theta1 =
0.6759
theta2 =
0.3773
theta1 =
0.6809
theta2 =
0.1659
theta1 =
0.7452
theta2 =
0.0474
theta1 =
0.7481
theta2 =
-0.3567
theta1 =
0.7219
theta2 =
-0.5588
theta1 =
0.5604
theta2 =
-1.3525
theta1 =
0.4964
theta2 =
-1.2835
theta1 =
0.4325
theta2 =
-1.4730
theta1 =
0.4700
theta2 =
-1.7439
theta1 =
0.3737
theta2 =
-1.9845
theta1 =
0.3106
theta2 =
-2.0505
theta1 =
0.0318
theta2 =
-2.1734
theta1 =
0.0152
theta2 =
-1.9838
theta1 =
-0.0658
theta2 =
-1.9572
theta1 =
-0.1132
theta2 =
-2.2180
theta1 =
-0.2356
theta2 =
-2.1507
theta1 =
-0.2926
theta2 =
-2.0439
theta1 =
-0.5013
theta2 =
-1.4823
theta1 =
-0.4597
theta2 =
-1.3331
theta1 =
-0.5074
theta2 =
-1.1372
theta1 =
-0.6111
theta2 =
-1.1826
theta1 =
-0.6742
theta2 =
-0.8791
theta1 =
-0.6875
theta2 =
-0.6985
theta1 =
-0.7066
theta2 =
0.0966
theta1 =
-0.6611
theta2 =
0.1294
theta1 =
-0.6481
theta2 =
0.3441
theta1 =
-0.7059
theta2 =
0.5006
theta1 =
-0.6787
theta2 =
0.8452
theta1 =
-0.6440
theta2 =
1.0039
theta1 =
-0.4603
theta2 =
1.6226
theta1 =
-0.4160
theta2 =
1.5644
theta1 =
-0.3532
theta2 =
1.6928
theta1 =
-0.3606
theta2 =
1.9049
theta1 =
-0.2543
theta2 =
2.0927
theta1 =
-0.1893
theta2 =
2.1237
theta1 =
0.0860
theta2 =
2.0879
theta1 =
0.0890
theta2 =
1.8784
theta1 =
0.1671
theta2 =
1.8094
theta1 =
0.2305
theta2 =
2.0604
theta1 =
0.3345
theta2 =
1.9421
theta1 =
0.3798
theta2 =
1.8277
theta1 =
0.5491
theta2 =
1.2628
theta1 =
0.5205
theta2 =
1.1614
theta1 =
0.5546
theta2 =
0.9810
theta1 =
0.6304
theta2 =
0.9619
theta1 =
0.6831
theta2 =
0.6429
theta1 =
0.6897
theta2 =
0.4592
theta1 =
0.6778
theta2 =
-0.3355
theta1 =
0.6286
theta2 =
-0.3528
theta1 =
0.6071
theta2 =
-0.5645
theta1 =
0.6620
theta2 =
-0.7384
theta1 =
0.6242
theta2 =
-1.0451
theta1 =
0.5876
theta2 =
-1.1805
theta1 =
0.4016
theta2 =
-1.7051
theta1 =
0.3648
theta2 =
-1.6522
theta1 =
0.3048
theta2 =
-1.7530
theta1 =
0.3025
theta2 =
-1.9350
theta1 =
0.1944
theta2 =
-2.0930
theta1 =
0.1304
theta2 =
-2.1068
theta1 =
-0.1359
theta2 =
-2.0021
theta1 =
-0.1324
theta2 =
-1.7936
theta1 =
-0.2070
theta2 =
-1.7078
theta1 =
-0.2764
theta2 =
-1.9417
theta1 =
-0.3698
theta2 =
-1.8082
theta1 =
-0.4093
theta2 =
-1.6947
theta1 =
-0.5589
theta2 =
-1.1425
theta1 =
-0.5364
theta2 =
-1.0560
theta1 =
-0.5647
theta2 =
-0.8863
theta1 =
-0.6273
theta2 =
-0.8516
theta1 =
-0.6744
theta2 =
-0.5305
theta1 =
-0.6780
theta2 =
-0.3480
theta1 =
-0.6521
theta2 =
0.4335
theta1 =
-0.6017
theta2 =
0.4419
theta1 =
-0.5766
theta2 =
0.6491
theta1 =
-0.6298
theta2 =
0.8301
theta1 =
-0.5886
theta2 =
1.1150
theta1 =
-0.5520
theta2 =
1.2381
theta1 =
-0.3688
theta2 =
1.7132
theta1 =
-0.3355
theta2 =
1.6629
theta1 =
-0.2778
theta2 =
1.7508
theta1 =
-0.2721
theta2 =
1.9176
theta1 =
-0.1651
theta2 =
2.0594
theta1 =
-0.1027
theta2 =
2.0655
theta1 =
0.1551
theta2 =
1.9336
theta1 =
0.1489
theta2 =
1.7311
theta1 =
0.2205
theta2 =
1.6397
theta1 =
0.2911
theta2 =
1.8598
theta1 =
0.3798
theta2 =
1.7211
theta1 =
0.4167
theta2 =
1.6080
theta1 =
0.5560
theta2 =
1.0612
theta1 =
0.5345
theta2 =
0.9800
theta1 =
0.5601
theta2 =
0.8142
theta1 =
0.6187
theta2 =
0.7744
theta1 =
0.6617
theta2 =
0.4559
theta1 =
0.6633
theta2 =
0.2765
theta1 =
0.6293
theta2 =
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theta1 =
0.5790
theta2 =
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theta1 =
0.5521
theta2 =
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theta1 =
0.6034
theta2 =
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theta1 =
0.5598
theta2 =
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theta1 =
0.5226
theta2 =
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theta1 =
0.3379
theta2 =
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theta1 =
0.3060
theta2 =
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theta1 =
0.2485
theta2 =
-1.7316
theta1 =
0.2409
theta2 =
-1.8995
theta1 =
0.1350
theta2 =
-2.0245
theta1 =
0.0743
theta2 =
-2.0228
theta1 =
-0.1745
theta2 =
-1.8637
theta1 =
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theta2 =
-1.6680
theta1 =
-0.2343
theta2 =
-1.5711
theta1 =
-0.3060
theta2 =
-1.7761
theta1 =
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theta2 =
-1.6297
theta1 =
-0.4262
theta2 =
-1.5143
theta1 =
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theta2 =
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theta1 =
-0.5325
theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
0.5665
theta1 =
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theta2 =
0.5615
theta1 =
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theta2 =
0.7565
theta1 =
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theta2 =
0.9438
theta1 =
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theta2 =
1.2091
theta1 =
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theta2 =
1.3185
theta1 =
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theta2 =
1.7201
theta1 =
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theta2 =
1.6510
theta1 =
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theta2 =
1.7186
theta1 =
-0.1966
theta2 =
1.8922
theta1 =
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theta2 =
1.9935
theta1 =
-0.0324
theta2 =
1.9800
theta1 =
0.2060
theta2 =
1.7780
theta1 =
0.1934
theta2 =
1.5900
theta1 =
0.2581
theta2 =
1.4835
theta1 =
0.3322
theta2 =
1.6685
theta1 =
0.4135
theta2 =
1.5085
theta1 =
0.4454
theta2 =
1.3882
theta1 =
0.5602
theta2 =
0.8192
theta1 =
0.5350
theta2 =
0.7481
theta1 =
0.5537
theta2 =
0.5792
theta1 =
0.6109
theta2 =
0.5222
theta1 =
0.6404
theta2 =
0.2031
theta1 =
0.6349
theta2 =
0.0297
theta1 =
0.5708
theta2 =
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theta1 =
0.5204
theta2 =
-0.6737
theta1 =
0.4861
theta2 =
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theta1 =
0.5307
theta2 =
-1.0556
theta1 =
0.4766
theta2 =
-1.3074
theta1 =
0.4350
theta2 =
-1.4057
theta1 =
0.2362
theta2 =
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theta1 =
0.2086
theta2 =
-1.6591
theta1 =
0.1482
theta2 =
-1.7090
theta1 =
0.1327
theta2 =
-1.8913
theta1 =
0.0276
theta2 =
-1.9582
theta1 =
-0.0292
theta2 =
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theta1 =
-0.2538
theta2 =
-1.6614
theta1 =
-0.2355
theta2 =
-1.4846
theta1 =
-0.2949
theta2 =
-1.3635
theta1 =
-0.3729
theta2 =
-1.5189
theta1 =
-0.4483
theta2 =
-1.3377
theta1 =
-0.4759
theta2 =
-1.2098
theta1 =
-0.5696
theta2 =
-0.6156
theta1 =
-0.5410
theta2 =
-0.5538
theta1 =
-0.5534
theta2 =
-0.3807
theta1 =
-0.6097
theta2 =
-0.3069
theta1 =
-0.6273
theta2 =
0.0156
theta1 =
-0.6153
theta2 =
0.1849
theta1 =
-0.5241
theta2 =
0.8710
theta1 =
-0.4735
theta2 =
0.8346
theta1 =
-0.4323
theta2 =
1.0074
theta1 =
-0.4708
theta2 =
1.2174
theta1 =
-0.4071
theta2 =
1.4472
theta1 =
-0.3617
theta2 =
1.5281
theta1 =
-0.1514
theta2 =
1.7754
theta1 =
-0.1287
theta2 =
1.6631
theta1 =
-0.0662
theta2 =
1.6858
theta1 =
-0.0422
theta2 =
1.8783
theta1 =
0.0620
theta2 =
1.8960
theta1 =
0.1152
theta2 =
1.8412
theta1 =
0.3194
theta2 =
1.4902
theta1 =
0.2938
theta2 =
1.3322
theta1 =
0.3454
theta2 =
1.1919
theta1 =
0.4278
theta2 =
1.3022
theta1 =
0.4940
theta2 =
1.0919
theta1 =
0.5151
theta2 =
0.9541
theta1 =
0.5776
theta2 =
0.3295
theta1 =
0.5446
theta2 =
0.2817
theta1 =
0.5478
theta2 =
0.1046
theta1 =
0.6019
theta2 =
0.0069
theta1 =
0.6023
theta2 =
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theta1 =
0.5812
theta2 =
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theta1 =
0.4531
theta2 =
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theta1 =
0.4036
theta2 =
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theta1 =
0.3531
theta2 =
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theta1 =
0.3819
theta2 =
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theta1 =
0.3059
theta2 =
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theta1 =
0.2564
theta2 =
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theta1 =
0.0366
theta2 =
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theta1 =
0.0233
theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
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theta1 =
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theta2 =
-1.5242
theta1 =
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theta2 =
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M =
struct with fields:
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colormap: []
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>> close all
>>
>>
Youtube Link : https://www.youtube.com/watch?v=1UK-cW535NY