trying to plot 3 variables in 3d

clc
clear all
theta= linspace(.01, .55) %for thetamax = 32 degrees
M=linspace(2,5)
gamma=1.4
lambda3=sqrt((((M.^2)-1).^2)-3.*(1+((gamma-1)/2).*(M.^2)).*(1+((gamma+1)/2).*(M.^2)).*(tan(theta)).^2);
chi=(1./(lambda3.^3)).*((((M.^2)-1).^3)-9.*(1+((gamma-1)./2).*(M.^2)).*(1+((gamma-1)/2).*(M.^2)+((gamma+1)./4).*(M.^4)).*((tan(theta)).^2));

beta= atan(((M.^2)-1+2.*lambda3.*cos((4.*pi+acos(chi))./3))./(3.*(1+((gamma-1)/2).*(M.^2)).*tan(theta)))

M1n=M.*sin(beta)
strength=1+((2*gamma)/(gamma+1)).*((M1n.^2) -1)

figure
surf(M, beta,strength)

im trying to 3d plot strength vs M and beta but it keeps saying strength isnt a matrix.

Answer 1

[Davide Masiello]

surf can handle only matrices, so this is what you want to do

theta= linspace(.01, .55); %for thetamax = 32 degrees
M=linspace(2,5);
gamma=1.4;
lambda3=sqrt((((M.^2)-1).^2)-3.*(1+((gamma-1)/2).*(M.^2)).*(1+((gamma+1)/2).*(M.^2)).*(tan(theta)).^2);
chi=(1./(lambda3.^3)).*((((M.^2)-1).^3)-9.*(1+((gamma-1)./2).*(M.^2)).*(1+((gamma-1)/2).*(M.^2)+((gamma+1)./4).*(M.^4)).*((tan(theta)).^2));
beta= atan(((M.^2)-1+2.*lambda3.*cos((4.*pi+acos(chi))./3))./(3.*(1+((gamma-1)/2).*(M.^2)).*tan(theta)));
[M,beta] = meshgrid(M,beta);
M1n=M.*sin(beta);
strength=1+((2*gamma)/(gamma+1)).*((M1n.^2) -1)

strength = 100×100

1.0327 1.0694 1.1065 1.1443 1.1825 1.2214 1.2607 1.3007 1.3411 1.3822 1.4237 1.4659 1.5085 1.5518 1.5956 1.6399 1.6848 1.7302 1.7762 1.8227 1.8698 1.9174 1.9656 2.0144 2.0636 2.1135 2.1639 2.2148 2.2663 2.3183 1.0154 1.0515 1.0881 1.1253 1.1630 1.2013 1.2401 1.2794 1.3193 1.3598 1.4007 1.4423 1.4843 1.5269 1.5701 1.6138 1.6580 1.7028 1.7481 1.7939 1.8403 1.8873 1.9348 1.9828 2.0314 2.0805 2.1302 2.1804 2.2311 2.2824 0.9992 1.0348 1.0709 1.1075 1.1447 1.1825 1.2208 1.2596 1.2989 1.3388 1.3792 1.4201 1.4616 1.5036 1.5462 1.5893 1.6329 1.6771 1.7218 1.7670 1.8128 1.8591 1.9059 1.9533 2.0012 2.0496 2.0986 2.1481 2.1982 2.2487 0.9840 1.0191 1.0548 1.0910 1.1277 1.1649 1.2027 1.2410 1.2798 1.3192 1.3591 1.3995 1.4404 1.4819 1.5239 1.5664 1.6095 1.6531 1.6972 1.7418 1.7870 1.8327 1.8789 1.9257 1.9730 2.0208 2.0691 2.1180 2.1674 2.2173 0.9698 1.0045 1.0397 1.0755 1.1117 1.1485 1.1858 1.2237 1.2620 1.3009 1.3403 1.3802 1.4207 1.4616 1.5031 1.5451 1.5876 1.6307 1.6742 1.7183 1.7630 1.8081 1.8537 1.8999 1.9466 1.9938 2.0416 2.0899 2.1386 2.1880 0.9566 0.9909 1.0257 1.0611 1.0969 1.1333 1.1701 1.2075 1.2454 1.2839 1.3228 1.3623 1.4022 1.4427 1.4837 1.5252 1.5673 1.6098 1.6529 1.6965 1.7406 1.7852 1.8303 1.8759 1.9221 1.9688 2.0160 2.0637 2.1119 2.1606 0.9444 0.9783 1.0127 1.0477 1.0831 1.1191 1.1556 1.1925 1.2300 1.2680 1.3065 1.3456 1.3851 1.4252 1.4657 1.5068 1.5483 1.5904 1.6330 1.6761 1.7197 1.7639 1.8085 1.8536 1.8993 1.9455 1.9921 2.0393 2.0870 2.1352 0.9330 0.9666 1.0007 1.0352 1.0703 1.1059 1.1420 1.1786 1.2157 1.2534 1.2915 1.3301 1.3692 1.4089 1.4490 1.4897 1.5308 1.5725 1.6146 1.6573 1.7004 1.7441 1.7883 1.8330 1.8782 1.9239 1.9701 2.0168 2.0640 2.1117 0.9225 0.9558 0.9895 1.0238 1.0585 1.0938 1.1295 1.1658 1.2025 1.2398 1.2776 1.3158 1.3546 1.3938 1.4336 1.4738 1.5146 1.5558 1.5976 1.6399 1.6826 1.7259 1.7696 1.8139 1.8586 1.9039 1.9497 1.9959 2.0427 2.0899 0.9128 0.9458 0.9792 1.0132 1.0476 1.0826 1.1180 1.1540 1.1904 1.2273 1.2647 1.3026 1.3411 1.3800 1.4194 1.4593 1.4997 1.5405 1.5819 1.6238 1.6662 1.7091 1.7524 1.7963 1.8407 1.8855 1.9309 1.9767 2.0230 2.0699

figure
surf(M, beta,strength)

Answer 2

[Voss]

clc
clear all
theta= linspace(.01, .55); %for thetamax = 32 degrees
M=linspace(2,5);
gamma=1.4;
lambda3=sqrt((((M.^2)-1).^2)-3.*(1+((gamma-1)/2).*(M.^2)).*(1+((gamma+1)/2).*(M.^2)).*(tan(theta)).^2);
chi=(1./(lambda3.^3)).*((((M.^2)-1).^3)-9.*(1+((gamma-1)./2).*(M.^2)).*(1+((gamma-1)/2).*(M.^2)+((gamma+1)./4).*(M.^4)).*((tan(theta)).^2));

beta= atan(((M.^2)-1+2.*lambda3.*cos((4.*pi+acos(chi))./3))./(3.*(1+((gamma-1)/2).*(M.^2)).*tan(theta)));

% transpose beta to get the appropriate matrix M1n:
M1n=M.*sin(beta.')

M1n = 100×100

1.0139 1.0293 1.0447 1.0600 1.0754 1.0907 1.1061 1.1215 1.1368 1.1522 1.1676 1.1829 1.1983 1.2137 1.2290 1.2444 1.2597 1.2751 1.2905 1.3058 1.3212 1.3366 1.3519 1.3673 1.3826 1.3980 1.4134 1.4287 1.4441 1.4595 1.0066 1.0218 1.0371 1.0523 1.0676 1.0828 1.0981 1.1133 1.1286 1.1438 1.1591 1.1743 1.1896 1.2048 1.2201 1.2353 1.2506 1.2658 1.2811 1.2963 1.3116 1.3269 1.3421 1.3574 1.3726 1.3879 1.4031 1.4184 1.4336 1.4489 0.9996 1.0148 1.0299 1.0451 1.0602 1.0754 1.0905 1.1057 1.1208 1.1360 1.1511 1.1662 1.1814 1.1965 1.2117 1.2268 1.2420 1.2571 1.2723 1.2874 1.3026 1.3177 1.3329 1.3480 1.3631 1.3783 1.3934 1.4086 1.4237 1.4389 0.9931 1.0082 1.0232 1.0383 1.0533 1.0683 1.0834 1.0984 1.1135 1.1285 1.1436 1.1586 1.1737 1.1887 1.2038 1.2188 1.2339 1.2489 1.2640 1.2790 1.2941 1.3091 1.3241 1.3392 1.3542 1.3693 1.3843 1.3994 1.4144 1.4295 0.9870 1.0019 1.0169 1.0318 1.0468 1.0617 1.0767 1.0917 1.1066 1.1216 1.1365 1.1515 1.1664 1.1814 1.1963 1.2113 1.2262 1.2412 1.2562 1.2711 1.2861 1.3010 1.3160 1.3309 1.3459 1.3608 1.3758 1.3907 1.4057 1.4207 0.9812 0.9961 1.0110 1.0258 1.0407 1.0556 1.0704 1.0853 1.1002 1.1150 1.1299 1.1448 1.1596 1.1745 1.1894 1.2042 1.2191 1.2340 1.2488 1.2637 1.2786 1.2934 1.3083 1.3232 1.3380 1.3529 1.3678 1.3826 1.3975 1.4124 0.9759 0.9907 1.0054 1.0202 1.0350 1.0498 1.0646 1.0794 1.0942 1.1089 1.1237 1.1385 1.1533 1.1681 1.1829 1.1977 1.2124 1.2272 1.2420 1.2568 1.2716 1.2864 1.3012 1.3159 1.3307 1.3455 1.3603 1.3751 1.3899 1.4047 0.9709 0.9856 1.0003 1.0150 1.0297 1.0444 1.0591 1.0738 1.0885 1.1033 1.1180 1.1327 1.1474 1.1621 1.1768 1.1915 1.2062 1.2209 1.2356 1.2504 1.2651 1.2798 1.2945 1.3092 1.3239 1.3386 1.3533 1.3680 1.3827 1.3975 0.9662 0.9809 0.9955 1.0101 1.0248 1.0394 1.0541 1.0687 1.0833 1.0980 1.1126 1.1273 1.1419 1.1565 1.1712 1.1858 1.2004 1.2151 1.2297 1.2444 1.2590 1.2736 1.2883 1.3029 1.3176 1.3322 1.3468 1.3615 1.3761 1.3908 0.9619 0.9765 0.9911 1.0056 1.0202 1.0348 1.0494 1.0639 1.0785 1.0931 1.1077 1.1222 1.1368 1.1514 1.1660 1.1805 1.1951 1.2097 1.2243 1.2388 1.2534 1.2680 1.2826 1.2971 1.3117 1.3263 1.3409 1.3554 1.3700 1.3846

strength=1+((2*gamma)/(gamma+1)).*((M1n.^2) -1);

figure
surf(M, beta,strength)
xlabel('M')
ylabel('beta')
zlabel('strength')