%% tilt-free seismometer primary mass
% estimate of pitch moment of inertia
% KLD Apr. 30, 2015
% =========== <-- cuboid mass
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% | | <--> pitch axis about which system rotates
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% =========== <-- cuboid mass
% parameters
M = 5; % [kg] cuboid mass
h = 0.025; % [m] cuboid height
d = 0.30; % [m] cuboid depth
w = 0.25; % [m] cuboid width
m = 0.5; % [kg] rod mass
l = 0.82; % [m] rod length
%% cuboid mass (one each at top and bottom)
% MOI about its own center of mass (axis parallel to system pitch axis)
I_cub_CoM = 1/12*M*(h^2+d^2);
% MOI about system pitch axis (apply parallel axis theorem)
I_cub = I_cub_CoM + M*(l/2+h/2)^2;
%% rod (one at each corner)
% MOI about its own center of mass (axis parallel to system pitch axis)
% infinitely thin approximation
I_rod_CoM = 1/12*m*l^2;
% MOI about system pitch axis (apply parallel axis theorem)
I_rod = I_rod_CoM + m*(d/2)^2;
%% total system moment of inertia
% sum of parts
I_pitch = 2*I_cub + 4*I_rod;
sprintf('Moment of inertia (pitch) = %2.1f kg m^2' , I_pitch)
%% Eigenfrequencies
% analytic equations from Malik's T000134
% parameters
m_tot = 2*M + 4*m;
g = 9.8; % [m/s^2]
L = l/2 + 0.15; % [m] wire length to suspension point
b = 0.001; % [w] distance from CoM to wire attachment
w_pitch = sqrt(m_tot*g*b*(L+b)/(I_pitch*L));
%w_roll = sqrt(m_tot*g*b*(L+b)/(I_roll*L)); (???) two wires!
%w_yaw = sqrt(m_tot*g*R1*R2/(I_yaw*L));
sprintf('Natural frequency (pitch) = %1.3f Hz' , w_pitch/(2*pi))