Use Eq. 8 to express the angular momentum of the con about its center of gravity (Eq. 5) in scalar form:
H_{cg} = H_{x}i + H_{y}j + H_{z}k
Here, we have
H_{x} = I_{xx}ω_{x}
H_{y} = I_{yy}ω_{y}
H_{z} = I_{yz}ω_{y}
Express the position and velocity of the con in rectangular components, and determine the moment of the linear momentum of the con about the center of gravity of the sub:
ρ_{con} = d_{y}j + d_{z}k
v_{con} = v_{x}j + v_{y}k
Use Eq. 7 to determine the angular momentum of the con about the center of gravity of the sub:
H_{A} = ρ_{con} × m_{c}v_{con} + H_{cg}
= (I_{xx}ω_{x}  d_{z}v_{y})i + (I_{yy}ω_{y}  d_{z}v_{x})j
+ (I_{yz}ω_{y}  d_{y}v_{x})k
