Dynamics of Mechanical Systems 2009 Part 2 potx
Dynamics of Mechanical Systems 2009 Part 2 potx
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AAA
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mp
BBB
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3
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ABC ABCABCCAB
BC A BA C CB A AC B
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()
=⋅×=×⋅=⋅×
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0593_C 02_ fm Page 34 Monday, May 6, 20 02 1:46 ... dt=−
()
[]
++
()()
[]
22
2
22
2θθ θ
θ
ωθ αω θ= d dt d dt d dtand = =
22
V
P
rn=ω...
Dynamics of Mechanical Systems 2009 Part 9 potx
... )
+
()
+−
()
+
12 12
12 12
12 4 12 1 12
12
1
1
1
2
2
2
22
22
2
1
22
1
2
2
1
22
12 2 1
2
m
m
mm
m
G
G
B
G
G
B
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ωω
ωω
lll
ll l
˙˙
˙˙˙
cos
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θθθθθ
44
12 1 12
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2
2
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2
2
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+
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++
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]
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2
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2
1
2
1
2
1
2
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12
3
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2
2
2
1
2
1
2
2
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2
2
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2
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2
2
mm...
Dynamics of Mechanical Systems 2009 Part 1 ppsx
...
AA AA==⋅=++
2
1
2
2
2
3
2
AAA
cosθ=
⋅
=
++
++
()
++
()
AB
AB
AB AB AB
AAA BBB
11 22 33
1
2
2
2
3
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1
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2
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An n n=−+ 524
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0593_C 02_ fm ... An=++
11 22 33
BBn Bn Bn=++
11 22 33
AB A A A B B B
AB AB AB
AB AB AB
AB AB
⋅= + +
()
⋅++
()
=⋅+⋅+⋅
+⋅+⋅+⋅
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11 22 33 11 22 3...
Dynamics of Mechanical Systems 2009 Part 3 pptx
... dt
2
2
ωαθω
22
2= +
∫
d
o
ωω αθ
22
2= +
o
0593_C04*_fm Page 84 Monday, May 6, 20 02 2:06 PM
86 Dynamics of Mechanical Systems
To see this, let c be expressed in terms of the unit vectors n
1
, n
2
, ...
3 m
12 m
60°
R Box
tttω= ++
()
++
()
2
12
2
3
24 nn nrad sec
R
n
n
n
3 ft
4 ft
12 ft
A
B
3
2
1
0593_C04*_fm Page 120 Monday, May 6, 20 02 2:06 PM
9...
Dynamics of Mechanical Systems 2009 Part 4 docx
... 1
=−
()
l
˙
cos sinθθ θ
aNN
O
XZ
2
111
2
1111
2
1
=−
()
+− −
()
[]
l
˙˙
cos
˙
sin
˙˙
sin
˙
cosθθθθ θθθθ
vvv aaa
G O GO G O GO
2 2 22 2 2 22
=+ =+
//
and
vnn
GO
22
22 322 1
22
/
˙
=×
()
=
()
ωω llθ
0593_C05_fm ... 3
21 1 32
11
4 12 10 123 10
12 15 3 4 8
3 624
22 3 1 3 3
1 123 31
322
8 3 12 16
120 120 30 180 24 32
72 24 48
+
()
+× +
()
=− + + − − −
+−−
nn nn
nnnn...
Dynamics of Mechanical Systems 2009 Part 5 pps
... ab
11 22 33 11 22 33
1111 121 2 1313
21 21 22 22 2 323
3131 322 2 3333
0593_C07_fm Page 20 3 Monday, May 6, 20 02 2: 42 PM
23 0 Dynamics of Mechanical Systems
where we have made use of Eqs. (7. 12. 4) and ... αβ
α
β
and
S
iα
=−
−
22 0 22
24 32 24
64 12 64
92 34 3 3 4
3 4 39 8 3 8
334 38 378
22 0 22
24 32 24
64 12 64
300
050
006
22 24 2...
Dynamics of Mechanical Systems 2009 Part 6 pdf
... βββ β βββ ββ
ββ
1
2
21
2
23
12
2
3 123
2
3 123
2
23
1
12
12 12 12
52 32ggll
1 12 123
12 0+
()
+
()( )
++
()
=ββββg l sin
53 32 12 53
13 12 32 12
12
23 23 1 32
33 1
2
21
2
23
12
2
3
()
+
()
++
()
+
()
[]
+
()
+
[]
+
()
+
()
[]
+
()
+
()
+
()
+
()
+
()
cos ... =
ll
ll
ll
22
2
20
12 2 12 1 1
12 22 2
12 22 2 2
nnnFT
nn n
nnFT
mg
mg
**
**
−
()
×−...
Dynamics of Mechanical Systems 2009 Part 7 pps
... x 12
00== =,
P
0
t
dt
∫
Qdt
y
t
0
∫
ll l ll lmv mv mv m mv m
yy y y 12 2
2
21
2
1
2 1 12 2 1 12+ =
()
+
()
−
()
+
()
ωω
ll21 12
1
2
1
()
=
()
mv m
y
ω
vvv
v
02 10 2 0 2
2 021 1
22 122
1 12 12 2 1 12
−−
()
+−
()
=
()
−
()
[]
+
()
−
()
−−
()
[]
+
()
ll ... ωωω
ω
=⋅⋅
=⋅⋅
1
2
1
2
ωω
ωωωω
In
I
BG
BG
I
ω
BG
K
G
BG
=+⋅⋅
1
2
1
2
2
vIωωωω
KM
G
=+ ++
()
1
2
1
2
2
11...
Dynamics of Mechanical Systems 2009 Part 8 docx
... h
Imr
=
()
+
()
−
()
−
()
=−
()
+−
+
12 12 12 12
12
22
222 222
23 22 2
2
ˆˆ
ωωωω
Lmhrh=− −
()
[]
3
Q
a
0
Ω
Q
O
Ω
0593_C10_fm Page 3 42 Monday, May 6, 20 02 2:57 PM
354
Dynamics of Mechanical Systems
System ... mx=
()
=
()
12 12
22
˙
WK k mv=
()
=
()
−∆ or 12 12 0
22
δ
vx km==
˙
δ
Wkd=−
()
12
2
Kmv k=
()
=
()
12 12
22
δ
W K kd k=−
()...
Dynamics of Mechanical Systems 2009 Part 10 pot
... km
ωωω
1
2
2
2
3
2
22 2 22 =−
()
()
=
()
=+
()
()
km km km,,
AAA
1
2
2
2
3
2
1++=
2
20
12
AA−=
−+ − =AAA
123
20
−+ =AA
23
20
2
AA A
12 3
12 2 2 12= = =,,
0593_C13_fm Page 453 Monday, May 6, 20 02 3 :21 ... 12
=
−
()
+
()
+
()
D
xxx
˙˙
˙˙ ˙˙
ξ
21 3
22 22
=
()
−
()
D
xx
˙˙
˙˙ ˙˙ ˙˙
ξ
3 123
12 2 2 12
=
−
()
+
()
+
()
D
xxx
˙˙
ξ
˙˙
ξ
1 121 23
23
12...