October 2011
Intermediate to advanced
749 pages
23h 36m
English
Content preview from Optimal Estimation of Dynamic Systems, 2nd Edition
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Review of Dynamic Systems 585
Therefore, the “forced” solution (including gravity) follows from Equation (A.53),
given by
⎡
⎢
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⎢
⎢
⎢
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x
1
(t)
x
2
(t)
x
3
(t)
x
4
(t)
x
5
(t)
x
6
(t)
⎤
⎥
⎥
⎥
⎥
⎥
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⎦
=
⎡
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⎣
100(t −t
0
) 00
010 0 (t −t
0
) 0
001 0 0 (t −t
0
)
000 1 0 0
000 0 1 0
000 0 0 1
⎤
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⎥
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⎥
⎥
⎦
⎡
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⎢
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x
1
(t
0
)
x
2
(t
0
)
x
3
(t
0
)
x
4
(t
0
)
x
5
(t
0
)
x
6
(t
0
)
⎤
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⎦
−
t
t
0
00(
τ
−t
0
) 001
T
gd
τ
or
⎡
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x
1
(t)
x
2
(t)
x
3
(t)
x
4
(t)
x
5
(t)
x
6
(t)
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⎦
=
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⎢
⎢
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⎢
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x
1
(t
0
)+x
4
(t
0
)(t −t
0
)
x
2
(t
0
)+x
5
(t
0
)(t −t
0
)
x
3
(t
0
)+x
6
(t
0
)(t −t
0
) −1/2g(t −t
0
)
2
x
4
(t
0
)
x
5
(t
0
)
x
6
(t
0
) −g(t −t
0
)
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⎦
which verify (again) the previous results and demonstrate the equivalence between
the preceding results of this section and conventional integration of the ...
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I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.