Dynamics of Mechanical Systems 2009 Part 4 docx

... + () 17 86 3 2 23 46 7 1 5 58 93 2 6 22 ./ 12 αα 0593_C05_fm Page 141 Monday, May 6, 2002 2:15 PM 144 Dynamics of Mechanical Systems and (5.6 .4) Similarly, the velocity and acceleration of O 2 are: (5.6.5) and ... n=− + −− +             r r r xy αω αω ω αω 2 24 4 24 an n n nn C xy x xy r r r r r r r =− − + +− +             + + +− +        ...

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... will be on holonomic systems because, as noted earlier, the vast majority of mechanical systems of interest are holonomic systems. 11 .4 Vector Functions, Partial Velocity, and Partial Angular Velocity Consider ... 355 The number of degrees of freedom of a mechanical system is the number of coordinates of the system if it were unrestricted minus the number of const...

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... kkkkkkkk kkkkkkkkk 141 32 2 3 14 23 142 13 24 3211 243 34 2 2 2 =−+− () =+−− () =− − + − () ˙ ε km ˆ ω km ˙ ˆˆˆ ˙ ˆˆˆ ˙ ˆˆ ˆ ˙ ˆ εεωεωεω εεωεωεω εεωεωεω εε kkkkkkk kkkkkkk kkkkkkk kk 141 3223 23 142 13 3211 243 41 12 12 12 12 = () +− () = () −+ ... εε εε εε εε ε ε ε ε εε εε εε 1 2 2 2 3 2 4 2 12 34 13 24 12 34 1 2 2 2 3 2 4 2 23 14 13 22 22 2 εεε εε εε ε ε ε ε kk kk kk k k k k...

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... Tuesday, May 7, 2002 9:07 AM 6 94 Dynamics of Mechanical Systems Section 19.5 Partial Angular Velocities P19.5.1: See Problems P19 .4. 1 to P19 .4. 6. Develop expressions for the partial angular velocity ... 2002 9: 14 AM 692 Dynamics of Mechanical Systems be the resulting degrees of freedom of each system? Would the presence of the end effector affect the relative adv...

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... Oscillator 44 7 13.6 Forced Vibration of a Damped Linear Oscillator 44 9 13.7 Systems with Several Degrees of Freedom 45 0 13.8 Analysis and Discussion of Three-Particle Movement: Modes of Vibration 45 5 ... Vibrations 43 9 13.1 Introduction 43 9 13.2 Solutions of Second-Order Differential Equations 43 9 13.3 The Undamped Linear Oscillator 44 4 13 .4 Forced Vibration o...

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... A ij T − = [] 1 ˆ det AA T− = 1 0593_C02_fm Page 40 Monday, May 6, 2002 1 :46 PM 46 Dynamics of Mechanical Systems P2 .4. 3: Given the unit vectors i and j and the vectors A and B as shown in Figure P2 .4. 3, let the magnitudes of A and ... 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)...

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... (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 have: (4. 9. 34) Using Eq. (4. 9.29) for values of ω x , ω y , and ω z , Eqs. (4. 9.33) ... 2002 2:15 PM 1 14 Dynamics of Mechanical Systems Problems Section 4. 2 Orientation of Rigid Bodies P4.2.1: In Eq. (4. 2.3), suppose that the orientation angles are α...

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... S iα =− −           22 0 22 24 32 24 64 12 64 92 34 3 3 4 3 4 39 8 3 8 3 34 38 378 22 0 22 24 32 24 64 12 64 300 050 006 22 24 24 03212 22 24 64 − −           =− −                     − −           300 050 006 22 ... 64 − −           =− −                     − −           300 050 00...

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... n z . P7 .4. 7: See Problems P7 .4. 5 and P7 .4. 6. Show that: FIGURE P7 .4. 2 A particle P in a Cartesian reference frame. FIGURE P7 .4. 4 Particles at the vertices of a triangle. O Z Y X Q(-1,2 ,4) P(2,-1,3) ... the directions of n x , n y , and n z . P7 .4. 8: See Problems P7.3.3 and P7 .4. 4. Find the following moments and products of inertia of S for O: P7 .4. 9: See Proble...

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... 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 in terms of a derivative of ... PM 3 24 Dynamics of Mechanical Systems (10.2.13) where t * is the time of action of F . The integrand of Eq. (10.2.13), F • v , is often...

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