Model-based Control

Moments of Inertia

https://en.wikipedia.org/wiki/Moment_of_inertia

https://en.wikipedia.org/wiki/List_of_moments_of_inertia

Solid cuboid

I = 1/12 M ( a^2 + b^2 )

Ideal

I_roll \approx I_yaw, I_pitch << I_roll, I_yaw

Interestingly, a sphere is not idael from the perspective of PID control/axis coupling.

Camera Panasonic

width	height	length
2.5 cm	5.5 cm	9 cm

axis	approximate moment of inertia	relative ratio
pitch	I \propto 2.5^2 + 5.5^2 = 36.5	1
roll	I \propto 5.5^2 + 9^2 = 111.25	3.05
yaw	I \propto 2.5^2 + 9^2 = 87.25	2.39

Camera GoPro Hero5

width	height	length
2.5 cm	4.5 cm	6.3 cm

axis	approximate moment of inertia	relative ratio
pitch	I \propto 2.5^2 + 4.5^2 = 26.5	1
roll	I \propto 4.5^2 + 6.3^2 = 59.94	2.26
yaw	I \propto 2.5^2 + 6.3^2 = 45.94	1.73

Camera Mobius

width	height	length
6 cm	2 cm	3 cm

axis	approximate moment of inertia	relative ratio
pitch	I \propto 6^2 + 2^2 = 40	1
roll	I \propto 2^2 + 3^2 = 13	0.325
yaw	I \propto 6^2 + 3^2 = 45	1.125

The Mobius camera style is not ideal, and thus more difficult to stabilize.