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Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB.
I plug in test values in both the formulas from the image and the code and they seem correct except from Iz in which the height (h) still appears and terms like 3h2r instead of h appear, Am I missing something in the integrations? Thank you in advance.
Code:
% Symbolic variables
syms r z theta R h M; % R (Radius) h(height) M(Mass)
% Ixx
unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First integration
dosx = int(unox,r,0,R); % Second Integration
tresx = int(dosx,theta,0,2*pi); % Third integration
Ix = tresx / ((pi*R^2*h)/3); % Division by the volume of a cone (Mass since densitiy is 1)
Ix = Ix*M % Setting up in terms of mass M
% Iyy
unoy = int((z^2+(r*cos(theta))^2)*r,z,r,h);
dosy = int(unoy,r,0,R);
tresy = int(dosy,theta,0,2*pi);
Iy = tresy / ((pi*R^2*h)/3);
Iy = Iy*M
% Izz
unoz = int(r^2*r,z,r,h);
dosz = int(unoz,r,0,R);
tresz = int(dosz,theta,0,2*pi);
Iz = tresz / ((pi*R^2*h)/3);
Iz = Iz*M
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