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Fundamental constants
c = 2.9979E8; %[m/s] Speed of light mu0 = 4*pi*1E-7; %[V*s/(A*m)] Permeability eps0 = 8.8542E-12; %[A*s/(V*m)] Permittivity G = 6.672E11; %[N*m2/kg2] Gravitation constant me = 9.109E-31; %[kg] Electron rest mass mp = 1.673E-27; %[kg] Proton rest mass e = 1.602E-19; %[C] Elementary charge k = 1.381E-23; %[J/K] Boltzmann constant h = 6.626E-34; %[J*s] Planck’s constant Me = 5.98E24; %[kg] Earth’s mass Re = 6.37E6; %[m] Earth’s radius Ms = 1.989E30; %[kg] Solar mass Rs = 6.966E8; %[m] Solar radius Md = 8E15; %[T*m3] Earth’s magnetic dipole moment R = 1.985E-3; %[kcal/(mole*K)]Gas constant
Spin axis, precession
Example 10.2, Orbital Mechanics for Engineering Students, 2nd Edition.
A cylindrical shell is rotating in torque-free motion about its longitudinal axis.
r = 1; % [m] l = 3; % [m] m = 100; % [kg] theta = 20; % [deg ]nutation angle % How long does it take the cylinder to precess through 180 ° if the % spin rate is 2*pi/radians per minute ws = 2*pi; % [rad/min] C = m*r^2 % [kg*m^2] A = 1/2*m*r^2 + 1/12*m*l^2
C = 100 A = 125.0000
A > C, Direct (prograde) precession
wp = C/(A - C)*ws/cosd(theta) % [rad/min]
wp = 26.7457
The time for the spin axis to precess through an angle of 180 ° is
t = pi/wp*60 % [sec]
t =
7.0477
Published with MATLAB® 7.10
Best Fit Solution,Straight Line Fit
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clear all clc T = [0,20,100,100,200,400,400,800,1000,1200,1400,1600]; R = [10.96,10.72,14.1,14.85,17.9,25.4,26,40.3,47,52.7,58,63]; plot(T,R,'r*'); title('Straight Line Fit'); xlabel('Temperature (deg C)'); ylabel('Resistivity (Ohm cm)'); sy = 0; sx = 0; sxy = 0; sx2 = 0; n = 12; for i=1:n sy = sy +R(i); sx = sx + T(i); sxy = sxy + T(i)*R(i); sx2 = sx2 + T(i)*T(i); end a = (sy*sx2-sx*sxy)/(n*sx2-sx^2); b = (n*sxy-sx*sy)/(n*sx2-sx^2); fprintf('\n\n Best Fit Coefficients') fprintf('\n x = %6.4f T + %6.4f \n',b,a) cm_fit =a+b*T; hold on; plot(T,cm_fit,'r'); legend('Data Points','Best Fit Solution','location','northwest');
Best Fit Coefficients x = 0.0337 T + 11.4695
Published with MATLAB® 7.10
Type K Thermocouple, Voltage vs Temperature
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% Polynomial Coefficients 0-500 °C[4] % Type K thermocouple c= [0,25.08355,7.860106e-2,-2.503131e-1,8.315270e-2,-1.228034e-2,... 9.804036e-4,-4.413030e-5,1.057734e-6,-1.052755e-8]; E= 0; % Measured Voltage difference in mv V = [1,E,E^2,E^3,E^4,E^5,E^6,E^7,E^8,E^9]; T_delta = c*V'; fprintf('Cold Bath Temp. = %0.3f C\n' ,T_delta ); fprintf('Cold Bath Temp. = %0.3f F\n\n' ,T_delta*1.8+32 ); E= 0.74; % Measured Voltage difference in mv V = [1,E,E^2,E^3,E^4,E^5,E^6,E^7,E^8,E^9]; T_delta = c*V'; fprintf('Room Bath Temp. = %0.3f C\n' ,T_delta ); fprintf('Room Bath Temp. = %0.3f F\n\n' ,T_delta*1.8+32 ); E= 3; % Measured Voltage difference in mv V = [1,E,E^2,E^3,E^4,E^5,E^6,E^7,E^8,E^9]; T_delta = c*V'; fprintf('Hot Bath Temp. = %0.3f C\n' ,T_delta ); fprintf('Hot Bath Temp. = %0.3f F\n\n' ,T_delta*1.8+32 );
Cold Bath Temp. = 0.000 C Cold Bath Temp. = 32.000 F Room Bath Temp. = 18.526 C Room Bath Temp. = 65.346 F Hot Bath Temp. = 73.576 C Hot Bath Temp. = 164.436 F
Published with MATLAB® 7.10
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