b - NTNU

3.3 Rigid-Body Equations of Motion
f b
b
X,Y,Z - force through o b expressed in b
m b
b
K,M,N - moment about o b expressed in b
b
v b/n u,v,w - linear velocity of o b relative o n expressed in b
b
b/n p,q,r - angular velocity of b relative to n expressed in b
r g
b
x g ,y g ,z g - vector from o b to CG expressed in b
Component form (SNAME 1950)
mu vr wq x g q 2 r 2 y g pq r z g pr q X
mv wp ur y g r 2 p 2 z g qr p x g qp r Y
mw uq vp z g p 2 q 2 x g rp q y g rq p Z
I x p I z I y qr r pqI xz r 2 q 2 I yz pr q I xy
my g w uq vp z g v wp ur K
I y q I x I z rp p qrI xy p 2 r 2 I zx qp rI yz
mz g u vr wq x g w uq vp M
I z r I y I x pq q rpI yz q 2 p 2 I xy rq p I zx
mx g v wp ur y g u vr wq N
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Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)