Dynamics of Mechanical Systems 2009 Part 6 pdf
Dynamics of Mechanical Systems 2009 Part 6 pdf
...
10 lb
16 cm
8 cm
5 kg
3 kg
0593_C08_fm Page 274 Monday, May 6, 2002 2:45 PM
266 Dynamics of Mechanical Systems
where a
2
is the n
2
component of a and T
3
is the n
3
component of T
*
; ... +
()
+
˙
˙
˙
sin
˙
cosθψφθφθnnn
123
0593_C08_fm Page 267 Monday, May 6, 2002 2:45 PM
260 Dynamics of Mechanical Systems
Setting moments of these force systems about O an...
Dynamics of Mechanical Systems 2009 Part 1 ppsx
... Analysis and Discussion of Three-Particle Movement:
Modes of Vibration 455
0593_ FM_fm Page 14 Tuesday, May 14, 2002 10:19 AM
6
Dynamics of Mechanical Systems
Two kinds of vectors occur so ...
FIGURE 1 .6. 2
Cartesian coordinate system.
Vn= s
s ==VnVVand /
O
O
Z
Y
X
P(x,y,z)
0593_C01_fm Page 6 Monday, May 6, 2002 1:43 PM
20 Dynamics of Mechanical Systems...
Dynamics of Mechanical Systems 2009 Part 2 potx
... Page 62 Monday, May 6, 2002 2:03 PM
68 Dynamics of Mechanical Systems
Then, from Eq. (3.7 .6) , the velocity of P may be expressed as:
(3.7.9)
Similarly, from Eq. (3.7.7), the acceleration of P ... sum of products of the elements of the ith row of A with the corresponding elements
of the jth column of B. Specifically,
(2.10.5)
where n is the number of columns of...
Dynamics of Mechanical Systems 2009 Part 3 pptx
... 113 Monday, May 6, 2002 2: 06 PM
1 26
Dynamics of Mechanical Systems
Using polar coordinates the constraint equation is:
(5.2.2)
The number of degrees of freedom of a
mechanical system
... Monday, May 6, 2002 2: 06 PM
Kinematics of a Rigid Body 89
Example 4 .6. 1: Effect of Earth Rotation
Equation (4 .6. 6) is useful for developing expressions for velocity and a...
Dynamics of Mechanical Systems 2009 Part 4 docx
... +
()
==−−
12334
567
133112
32 2 13
223
0 3 10 4 15 3 8
4 8 0 12 12 16
30 60 24 32
1131
144 192−+nn
Mnnn
O
=−− 160 30 168
12 3
ftlb
0593_C 06_ fm Page 168 Monday, May 6, 2002 2:28 PM
160 Dynamics of Mechanical Systems
a. ... is:
or
(6. 3. 16)
According to Eq. (6. 3 .6) , M
O
and M
Q
are related by the expression:
(6. 3.17)
By substituting from Eqs. (6. 3.14), (6. 3.15), and...
Dynamics of Mechanical Systems 2009 Part 5 pps
... Monday, May 6, 2002 2:42 PM
188 Dynamics of Mechanical Systems
P6.2.2: See Problem P6.2.1. Find the moment of F about points O, A, and B of Figure P6.2.1.
Express the results in terms of n
x
, n
y
, ... results in terms of the unit vectors
n
1
, n
2
, and n
3
shown in Figure P6.5.3.
6. 6 Wrenches
P6 .6. 1: See Problems P6.5.1 and P6.3.1. For the force system of Problems P...
Dynamics of Mechanical Systems 2009 Part 7 pps
... 329 Monday, May 6, 2002 2:57 PM
330 Dynamics of Mechanical Systems
The left side of Eq. (10 .6. 2) may be recognized as the power of F (see Eq. (10.4.2)). The
right side of Eq. (10 .6. 2) may be expressed ... free-body diagram of B may be constructed as in Figure 9 .6. 6.
Recall from Eqs. (8 .6. 5) and (8 .6. 6) that F
*
and T
*
may be expressed as:
(9 .6. 24)
FIGURE 9 .6....
Dynamics of Mechanical Systems 2009 Part 8 docx
... Page 3 36 Monday, May 6, 2002 2:57 PM
360 Dynamics of Mechanical Systems
Thus, Eq. (11.4.2) may be expressed in the form:
(11.4.5)
From Eq. (11.4.2), we see that the partial rate of change of the ... Page 370 Monday, May 6, 2002 2:59 PM
364 Dynamics of Mechanical Systems
Observe in Eq. (11.5.1) that the number of generalized forces is the same as the degrees
of fr...
Dynamics of Mechanical Systems 2009 Part 9 potx
... May 6, 2002 2:59 PM
428 Dynamics of Mechanical Systems
In Section 11.12 (Eq. (11.12.17)), we found the kinetic energy of the system to be:
(12.3.25)
where, as before, m is the mass of each particle, ... x
θ
θθ=−
()
−+++
()
26
123
sin sinl
d
dt
K
q
K
q
Frxxx
rr
r
∂
∂
−
∂
∂
==
˙
,,,
123
θ
0593_C12_fm Page 428 Monday, May 6, 2002 3:11 PM
4 06 Dynamics of Mechani...
Dynamics of Mechanical Systems 2009 Part 10 pot
... Page 4 56 Monday, May 6, 2002 3:21 PM
4 36 Dynamics of Mechanical Systems
References
12.1. Kane, T. R., Dynamics of nonholonomic systems, J. Appl. Mech., 28, 574, 1 961 .
12.2. Kane, T. R., Dynamics, ... Monday, May 6, 2002 3:21 PM
450 Dynamics of Mechanical Systems
Equation (13 .6. 1) then takes the form:
(13 .6. 3)
From Eqs. (13.2.27) through (13.2.31), we see that...
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