Chapter 3 - Dynamics of Marine Vessels

18
3.3.1 Nonlinear Equations of Motion
Property (Coriolis and Centripetal Matrix): For a rigid body moving
through an ideal fluid the Coriolis and centripetal matrix can always be
parameterized such that it is skew-symmetric, that is
If M is nonsymmetric, we write M as the sum of a symmetric and skewsymmetric
matrix:
where
C −C , ∀ ∈ 6
M 1
2 M M 1
2 M − M
M 0 T 1
2 M 1
2 M̄ 0
M̄ M̄ 1
2 M M 0
This implies that we can compute C from
M̄ M̄ 0
1
2 M − M 0
Ivar Ihle – TTK4190 Spring 2006