write me a method to calculate reaction wheel torque authority for a pyramid configuration of four reaction wheels in matlab

To calculate reaction wheel torque authority for a pyramid configuration of four reaction wheels in Matlab, we can use the following method:

  • Define the given parameters (assuming that the required inputs are mass, radius, and angular velocity):
main.m
m = ...; % mass of satellite [kg]
r = ...; % distance from the center of mass [m]
w = ...; % angular velocity [rad/s]
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  • Define the moment of inertia matrix (assuming that the satellite has a pyramid configuration of four reaction wheels):
main.m
Ixx = ...; % moment of inertia around x-axis [kg.m^2]
Iyy = ...; % moment of inertia around y-axis [kg.m^2]
Izz = ...; % moment of inertia around z-axis [kg.m^2]

I = [ Ixx   0    0  ;
        0  Iyy   0  ;
        0    0  Izz ];
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  • Calculate the angular momentum:
main.m
h = I * w; % angular momentum [kg.m^2/s]
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  • Calculate the torque authority:
main.m
J = [ r/2   r/2   0    0   ;
        0     0   r/2  r/2 ;
       -r/4   r/4  r/4 -r/4 ];

T = J * h; % torque authority [N.m]
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The resulting torque authority T is a vector of length 3 that represents the torque authority around the x, y, and z axes, respectively.

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