Geoscience Reference
In-Depth Information
mass centre above the water-line;
ʺ
ʷ
is the reducing coef
cient of transverse-hor-
izontal oscillation; h and
is the height and length of harmonic wave, respectively.
The ship moving on sea surface is de
ʻ
ned by numerous factors which were listed
above as well by Earth magnetic
field, inaccuracy of navigation devices and errors
in the measurements of distance up to the lightships. This implies that ship moving
has stochastic character. Let the ship start his moving from point O of rectangular
system of coordinates
φ
O
ʻ
at time t = 0. It is supposed that ship shift on the axis
φ
is forced by regular factor shifting it by
ʔφ ≥
0 at time unit. Ship shift
ʔʷ
on axis
ʻ
has stochastic character with distribution
(
)
¼
Z
Dk
2
a
Dk
r
1
2
ð
a
z
Þ
P
ðDg
\
DkÞ
¼
U
p
exp
p
2
dz
;
p
r
1
2
are the average of distribution and dispersion of
where a and
˃
ʔʷ
, respectively.
As a result, the ship will be in coordinates (
φ
T
,
ʷ
) at time t=Tunder the
nal
goal to achieve a point (
φ
T
, 0). It is supposed that axis
φ
and axis t are identical.
Time T for the ship moving from point O to point (
.
Let us divide the ship path into intervals from which it passes during time periods
φ
T
,
ʷ
) equals to T=
φ
T
/
ʔφ
t
1
,
+t
n+1
= T) and it is supposed that a = 0 when t = 0. Then at the moment
t
1
the ship will be to the position (
…
, t
n+1
(t
1
+
···
t
p
, u
p
is the p-fractile of
normal distribution). At this moment, the law of the ship coordinate change is
u
p
r
φ
t1
,
ʷ
1
)where(
gjj
a
1
Dk
r
P
ðDg
\
DkÞ
¼
U
;
where a
1
=
T).
The ship has inertia factor and its mobility is restricted by |a|
ʷ
1
/(t
1
−
≤
h where h is some
constant particularly equal to the tangent of the turn corner that is permissible for
this ship type. We have
u
p
r
p
¼ p
P
gj
\
t
1
and as a result
u
p
r
p
ht
2
;
t
1
where t
2
¼ T
t
1
.
Then dispersion minimum of the ship deviation from position (
φ
T
, 0) at the
moment T under n = 1 is achieved when the management is realized at the moment
y
p
5y
2
t
1
¼ T
þ
0
:
T
þ
0
:
25y
2
;
y ¼ u
p
r=
h
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