31 
Figure 6: Degrees of freedom in the cartesian coordinate system 
The state variables considered for position and movement are given in Table 1 (variables derived in 
terms of time are denoted with an apostrophe [*]). 
General des 
ignation 
State variables 
Reference 
system 
Explanation 
Unit 
Latitude 
Longitude 
xe 
Yb 
Bottom 
Position of ship reference point 
deg 
Speed over 
ground 
X’b 
Yb 
Bottom 
Speed of ship reference point 
kn 
Heading 
Yb 
Water 
Angle between xb and xs around Zb 
deg 
Rate of turn 
Yb 
Water 
Rotational speed around the z-axis 
deg/s 
Speed through 
water 
x’w 
yw 
Water 
Speed of ship reference point 
kn 
Depth 
Zw 
Water 
Distance to bottom in z direction 
m 
Heeling 
as 
Ship 
Rotation around the x-axis in relation to 
the x-y plane of the reference system 
“water 1 
deg 
Trim 
ßs 
Ship 
Rotation around the y-axis in relation to 
the x-y plane of the reference system 
“water 1 
deg 
Table 1 : 
State variables to describe position and movement