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