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...

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... 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...

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... 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...

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... 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...

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... + () ==−− 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...

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... 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...

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... 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....

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... 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...

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... 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...

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... 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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