b - NTNU

3.1.1 Translational Motion about CG
r g/n r b/n r g #
{n} is inertial
r g/i r b/i r g #
Time differentiation of
reference frame {b} gives
v g/n v b/n
For a rigid body, CG satisfies
b
d
dt
r g 0 #
r g/n
in a moving
b
d
dt
r g b/n r g #
v g/n v b/n b/n r g #
f g i d
dt
mv g/i
i d
dt
mv g/n
b d mv dt g/n m b/n mv g/n
mv g/n b/n v g/n # b
mv g/n
r g
CO
r b/i
r g/i
{i}={n} inertial frame
{b}
Body-fixed reference frame {b} is fixed in
the point CO and rotating with respect
to the inertial frame {i}
Translational Motion about CG Expressed in {b}
S b
b/n
v b b
g/n f g
#
CG
5
Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)