Dynamics of Mechanical Systems 2009 Part 10 pot

... 465 and (13 .10. 13) Hence, from Eq. (13.11.2), 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 ... May 6, 2002 3:21 PM 436 Dynamics of Mechanical Systems References 12.1. Kane, T. R., Dynamics of nonholonomic systems, J. Ap...

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... 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 A and the number of rows of B. A aa an aa an aa a mn ... 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 may be...

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... Then , , , and are: or (11 .10. 15) or (11 .10. 16) (11 .10. 17) and (11 .10. 18) From Eq. (11 .10. 12) the partial velocities of G 1 and G 2 and the partial angular velocities of B 1 and B 2 are (see ... 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 eac...

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... nnn Cn = =°+°=+ = 15 12 60 12 60 6 10 392 10 x yzyz x N N N cos sin . RABC n n n n nn n =++= + + () + =++ 15 6 10 392 10 10 21 10 392 yy z x xy z N N . . R = () + () + () [] =10 21 10 392 25 47 22 2 12 / NN 0593_C02_fm ... PM 0593_ FM_fm Page 10 Tuesday, May 14, 2002 10: 19 AM 10. 4 Power 327 10. 5 Kinetic Energy 327 10. 6 Work–Energy Principles 329 10. 7 Elementary...

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... 84 Dynamics of Mechanical Systems Observe that θ measures the rotation of B in R. It is also a measure of the orientation of B in R. In this context, the angular velocity of B in R is ... May 6, 2002 2:06 PM 126 Dynamics of Mechanical Systems Using polar coordinates the constraint equation is: (5.2.2) The number of degrees of freedom of a mechanical syste...

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... lines of action passing through points P i of the particles and bodies of V as in Figure 6.3.2. Then, S is called a system of forces . Systems of forces — particularly systems ... coordinates of the instant center C of B and the velocity of point Q of B whose coordinates are (2, 4). Express the velocity of Q in terms of n x and n y . P5.7.2:...

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... obtain: (7 .10. 16) (7 .10. 17) (7 .10. 18) (7 .10. 19) where we have used Eqs. (7 .10. 11) and (7 .10. 12). By comparing Eqs. (7 .10. 16) and (7 .10. 19) and by recalling that I ik is symmetric, we have: (7 .10. 20) Then, Eqs. (7 .10. 14) ... PM 190 Dynamics of Mechanical Systems a. Determine the resultant R of this system of forces. b. Find the moments of the force system abo...

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... PM 260 Dynamics of Mechanical Systems Setting moments of these force systems about O and Q equal to zero leads to the equations: (8 .10. 9) and (8 .10. 10) By substituting from Eq. (8 .10. 4) to (8 .10. 8), ... P G 10 in. 20 in. Y A X O G 10 in. 20 in. 5 in 0593_C07_fm Page 238 Monday, May 6, 2002 2:42 PM 258 Dynamics of Mechanical Systems 8 .10 Double-Rod P...

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... ⋅m 0593_C10_fm Page 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) ... in terms of a derivative of the square of the velocity of P. That is, (10. 6.3) From Eqs. (10. 4.1) and (10. 4.2) we recognize the left side of Eq. (10. 6.2) a...

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... 180°)? P10.6.8: Repeat Problems P10.6.5 to 10. 6.7 if the mass of P is 10 lb instead of 5 lb. P10.6.9: Repeat Problems P10.6.5 to 10. 6.7 if the length ᐉ of the pendulum is 4 ft. FIGURE P10.5.5 Triple-rod ... 2:59 PM 352 Dynamics of Mechanical Systems P10 .10. 8: Repeat Problem P10 .10. 6 if just before collision, instead of being stopped, the automobile is moving toward t...

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