Dynamics of Mechanical Systems 2009 Part 9 potx

... θ 0 593 _C11_fm Page 396 Monday, May 6, 2002 2: 59 PM 398 Dynamics of Mechanical Systems Example 11.12.4: Spring-Supported Particles in a Rotating Tube For another example illustrating the use of ... ˙ x ˙ y ˙ z ˙ X ˙ Y ˙ Z 0 593 _C11_fm Page 404 Monday, May 6, 2002 2: 59 PM 402 Dynamics of Mechanical Systems 11.3. Kane, T. R., Analytical Elements of Mechanics, Vol. 1...

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... 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 A and the number of rows of ... , δ ij j i VV= 0 593 _C02_fm Page 38 Monday, May 6, 2002 1:46 PM 76 Dynamics of Mechanical Systems Determine the velocity and acceleration of P when θ is (a) 0˚; (b)...

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... Chapter 9 Principles of Impulse and Momentum 2 79 9.1 Introduction 2 79 9.2 Impulse 2 79 9.3 Linear Momentum 280 9. 4 Angular Momentum 282 9. 5 Principle of Linear Impulse and Momentum 285 9. 6 Principle ... Principle of Angular Impulse and Momentum 288 9. 7 Conservation of Momentum Principles 294 9. 8 Examples 295 9. 9 Additional Examples: Conservation of Momentum 301...

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... form: (4 .9. 31) Let a B be expressed as: (4 .9. 32) Then, by substituting from Eqs. (4 .9. 19) , (4 .9. 22), (4 .9. 23), (4 .9. 31), and (4 .9. 32) into (4 .9. 30), we have: (4 .9. 33) Also, from Eq. (4 .9. 20) we ... sinθθθ 0 593 _C04*_fm Page 113 Monday, May 6, 2002 2:06 PM 126 Dynamics of Mechanical Systems Using polar coordinates the constraint equation is: (5.2.2) The numbe...

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... 32 1131 144 192 −+nn Mnnn O =−−160 30 168 12 3 ftlb 0 593 _C06_fm Page 168 Monday, May 6, 2002 2:28 PM 160 Dynamics of Mechanical Systems a. Locate or identify the instant center of zero velocity of the ... FIGURE 6.3.1 A mechanical system. FIGURE 6.3.2 A set of forces acting on a mechanical system. 0 593 _C06_fm Page 165 Monday, May 6, 2002 2:28 PM 172 Dynamics...

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... rnr rnr I nI I ii i ×× () =×× () =×× () = =⋅ =⋅ == = ∑∑ ∑ αα αα αα 11 1 α α α α α α α 0 593 _C07_fm Page 2 29 Monday, May 6, 2002 2:42 PM 190 Dynamics of Mechanical Systems a. Determine the resultant R of this system of forces. b. Find the moments of the force system ... i i N ααωωωω 11 Ipnp a PO D a m=×× () 0 593 _C07_fm Page 199 Monday, May 6, 2002 2:42 PM 188 Dynamics...

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... 0 593 _C08_fm Page 2 59 Monday, May 6, 2002 2:45 PM 256 Dynamics of Mechanical Systems The mass center G moves in a circle with radius ᐉ/2. The acceleration of G is: (8 .9. 2) Due to the symmetry of ... + () + ˙ ˙ ˙ sin ˙ cosθψφθφθnnn 123 0 593 _C08_fm Page 267 Monday, May 6, 2002 2:45 PM 260 Dynamics of Mechanical Systems Setting moments of these force systems about...

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... ω 0 593 _C 09_ fm Page 299 Monday, May 6, 2002 2:50 PM 308 Dynamics of Mechanical Systems In the T direction, the momenta of each particle are conserved, producing the equations: (9. 11.4) and (9. 11.5) Finally, ... Principles of Impulse and Momentum 303 Equating the expressions of Eqs. (9. 9.6) and (9. 9.7), we find to be: (9. 9.8) 9. 10 Impact: Coefficient of Restitution T...

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... n 0 593 _C11_fm 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 freedom of the ... L T 0 593 _C11_fm Page 3 69 Monday, May 6, 2002 2: 59 PM 362 Dynamics of Mechanical Systems fixed point O in R. Let the coordinates of P be (x, y, z), the X, Y, Z Car...

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... − () =gCl ᐉ θ 0 593 _C13_fm Page 4 59 Monday, May 6, 2002 3:21 PM 462 Dynamics of Mechanical Systems and then (13 .9. 19) or (13 .9. 20) Regarding the limits of the integral of Eq. (13 .9. 9) we have from Eq. (13 .9. 10) ... x )) + () [] = () −+ () xx km 23 1 12 22ξ 0 593 _C13_fm Page 456 Monday, May 6, 2002 3:21 PM 436 Dynamics of Mechanical Systems References 12.1. Kan...

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