Dynamics of Mechanical Systems 2009 Part 1 ppsx
Dynamics of Mechanical Systems 2009 Part 1 ppsx
...
AAn An 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
⋅= + +
()
⋅++
()
=⋅+⋅+⋅
+⋅+⋅+⋅
+⋅+⋅
11 22 33 11 22 33
11 1 1 12 1 2 13 1 3
212 1 32 3 2 23 2 3
313 1 32 3 2
nnnnnn
nn ... Forces 375
11 .9 Generalized Forces: Inertia (Passive) Forces 377
11 .10 Examples 379
11 .11 Potential Energy 389
11 .12 Use of Kinetic Energy to
Obtain Genera...
Dynamics of Mechanical Systems 2009 Part 2 potx
... Eqs. (2 .11 .6) and (2 .11 .7).
By substituting from Eqs. (2 .11 .6) and (2 .11 .7) into Eqs. (2 .11 .1) and (2 .11 .2), we obtain:
(2 .11 .8)
and
(2 .11 .9)
Hence, we have:
(2 .11 .10 )
Observe that Eq. (2 .11 .10 ) ... =−
AAA
BBB
CCC
BBB
CCC
AAA
CCC
AAA
BBB
mp
BBB
AAA
CCC
AAA
CCC
BBB
CCC
BB
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12 3
12...
Dynamics of Mechanical Systems 2009 Part 3 pptx
... ⋅
+⋅
n
n
nn
n
nn
n
nn n
n
nn
n
nn
1
2
31
3
12
1
23 1
3
13
1
22
nn nn
11 13
10 ⋅= ⋅= and
d
= 0 and
1
n
n
n
nn
n
11
31
3
dt
d
dt
d
dt
⋅⋅=−⋅
RB
d
dt
d
dt
d
dt
ωω× = ⋅
+⋅
+⋅
n
n
nn
n
nn
n
nn
1
1
11
1
22
1
33
RB
ddtωω× ... obtain:
(4 .13 .10 )
RB
ωω= + +ωωω
11 22 33
nnn
R GRB RGRB
rrVn V n=× =×−
()
ωωωω
21...
Dynamics of Mechanical Systems 2009 Part 4 docx
...
aNN
G
XZ
1
111
2
11 11
2
1
2=
()
−
()
+− −
()
[]
l
˙˙
cos
˙
sin
˙˙
sin
˙
cosθθθθ θθθθ
vn ann
OO
22
1 11 1 11 1
2
13
==−lll
˙˙˙˙
θθθ and
vNN
O
XZ
2
11 1
=−
()
l
˙
cos sinθθ θ
aNN
O
XZ
2
11 1
2
11 11
2
1
=−
()
+− ... +
()
==−−
12 334
567
13 311 2
32 2 13
223
0 3 10 4 15 3 8
4 8 0 12 12 16
30 60 24 32
11 31
144 19 2−+nn
Mnnn
O
=− 16 0 30 16 8
12 3
ftlb
059...
Dynamics of Mechanical Systems 2009 Part 5 pps
... ab ab
11 22 33 11 22 33
11 11 1 212 13 13
212 1 2222 2323
313 1 3222 3333
0593_C07_fm Page 203 Monday, May 6, 2002 2:42 PM
230 Dynamics of Mechanical Systems
where we have made use of Eqs. (7 .12 .4) ... z
III
III
III
=++
=++
=++
Innnn
Innnn
Innnn
1 11 1 12 2 13 3 1
2 21 1 22 2 23 3 2
3 31 1 32 2 33 3 3
PO
jj
PO
jj
PO
jj
III I
III I
III I
=++=
=++=
=++=
In
i
PO
ij i...
Dynamics of Mechanical Systems 2009 Part 6 pdf
... 8 .10 .4
Free-body diagram of rod B
2
.
nnnnnn
nnnnnn
11 1 1 1 2 21 2 1 2 2
12 1 1 1 2 22 2 1 2 2
=+ =+
=− + =− +
cs cs
sc sc
,
,
nc s nc s
ns c ns c
1 1 11 1 12 1 2 21 2 22
2 1 11 1 12 2 2 21 2 22
=− =−
=− ...
nnnnnn
nnnn nn
11 2 1 21 2 1 22 21 2 1 11 2 1 12
12 2 1 21 2 1 22 22 2 1 11 2 1 22
=− =+
=+ =−+
−− −−
−− −−
cs cs
sc sc
,
,
Fa...
Dynamics of Mechanical Systems 2009 Part 7 pps
... m
y
ω
vvv
v
02 10 2 0 2
20 21 1
2 212 2
11 2 12 2 11 2
−−
()
+−
()
=
()
−
()
[]
+
()
−
()
−−
()
[]
+
()
ll l l
llll
ωω ω ω
ωωωω
12 2 11 2
02 1 1
()
−−
()
[]
=
()
v ll lωω ω
v
01 2
512 11 12=
()
+
()
llωω
v
012
23=
()
+llωω
ωω ... ii
i
N
i
i
N
i
Gi
=+⋅×+×
()
=
+⋅×
+×
()
=++
===
===
∑∑∑
∑∑∑
1
2
1
2
1
2
1
2
1
2
0
1
2
2
11
2
1
1
2
11
2
2
vv...
Dynamics of Mechanical Systems 2009 Part 8 docx
... be:
(11 .7 .1)
and
(11 .7.2)
(11 .7.3)
(11 .7.4)
where n
1
, n
2
, and n
3
are the unit vectors of Figures 11 .7.2 and 11 .7.3. From Eqs. (11 .4.4)
and (11 .4 .15 ) we obtain the partial velocities and partial ... ,
x
P
x
P
x
PP
x
P
x
P
x
P
P
x
P
x
P
x
PP
x
x
1
1
2
1
3
11
1
2
2
2
3
2
3
1
3
2
3
3
3
11 2
12 2
1
00
002
00
====+
()
== ==+
()
===
θ
θ
θ
l
l
33
3
32
=+
()
l...
Dynamics of Mechanical Systems 2009 Part 9 potx
...
Generalized Dynamics: Kane’s Equations and Lagrange’s Equations
419
or
(12 .2 .16 )
and
or
(12 .2 .17 )
In Sections 11 .10 and 11 .12 , Eqs. (11 .10 . 21) , (11 .10 .22), (11 .12 .14 ), and (11 .12 .15 ), we
found ... Figure P 11. 11. 9. Repeat Problems P 11. 11. 6 and P 11. 11. 7
finding the potential energies for the relative orientation angles.
P 11. 11. 10: Use the results of P...
Dynamics of Mechanical Systems 2009 Part 10 pot
... F(A, ψ) is:
(13 .10 .14 )
Then, Eqs. (13 .10 .4) and (13 .10 .5) become:
(13 .10 .15 )
and
(13 .10 .16 )
Upon integration of Eqs. (13 .10 .15 ) and (13 .10 .16 ) we obtain:
(13 .10 .17 )
and
(13 .10 .18 )
where φ
0
is ... (13 .8 .11 ), (13 .8 .12 ), and (13 .8 .13 ) in the
form of Eqs. (13 .8 .14 ), (13 .8 .15 ), and (13 .8 .16 ). The derivatives of ξ
1
, ξ
2
, and ξ
3
may be
e...
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