Dynamics of Mechanical Systems 2009 Part 7 pps
Dynamics of Mechanical Systems 2009 Part 7 pps
... 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 in terms of a ... 324 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 cal...
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Dynamics of Mechanical Systems 2009 Part 1 ppsx
... 0593_C02_fm Page 17 Monday, May 6, 2002 1:46 PM 7. 3 Moments and Products of Inertia 200 7. 4 Inertia Dyadics 203 7. 5 Transformation Rules 205 7. 6 Parallel Axis Theorems 206 7. 7 Principal Axes, ... The Rolling Circular Disk 2 67 8.14 Closure 270 References 270 Problems 271 Chapter 9 Principles of Impulse and Momentum 279 9.1 Introduction 279 9.2 Impulse 279 9.3 Linea...
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Dynamics of Mechanical Systems 2009 Part 5 pps
... Mechanical Systems (7. 8.3) Expanding the determinant, we obtain: (7. 8.4) The coefficients of Eq. (7. 8.4) are seen to be the parameters I I , I II , and I III of Eqs. (7. 7.13), (7. 7.14), and (7. 7.15). By ... contributions of the individual particles. That is, for a system S of N particles we have: (7. 4.13) 7. 5 Transformation Rules Consider again the definition of the s...
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Dynamics of Mechanical Systems 2009 Part 2 potx
... 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 may be expressed as: (3 .7. 10) 3.8 ... 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 colu...
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Dynamics of Mechanical Systems 2009 Part 3 pptx
... 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 ... written at the base of the graph. Therefore, from Eq. (4 .7. 6) we have: (4 .7. 7) From the configuration graph of Figure 4 .7. 4 we have (see Eq. (4.4.1)): (4 .7. 8) Hence, R ω B is: (4...
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Dynamics of Mechanical Systems 2009 Part 4 docx
... PM 180 Dynamics of Mechanical Systems Therefore, by combining Eqs. (6 .7. 8) and (6 .7. 9), we obtain: (6 .7. 10) where the sum k 1 + k 2 is now the equivalent spring modulus. Observe that Eq. (6 .7. 10) ... Figure P5 .7. 1. Determine the 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 te...
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Dynamics of Mechanical Systems 2009 Part 6 pdf
... Figure P7.3.3, find the following moments and products of inertia: P7.3.6: See Problems P7.2.10, P7.3.3, P7.3.4, and P7.3.5. Show that: P7.3 .7: See Problems P7.2.5, P7.2.6, P7.2 .7, and P7.3.3. ... vectors P7.4.10: See Problems P7.2.5, P7.2.6, P7.3 .7, P7.4.4, and P7.4.9. Let n a and n b be the unit vectors of Problem P7.4.9. Find the following moments and products of inertia of S...
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Dynamics of Mechanical Systems 2009 Part 8 docx
... be: (11 .7. 1) and (11 .7. 2) (11 .7. 3) (11 .7. 4) where n 1 , n 2 , and n 3 are the unit vectors of Figures 11 .7. 2 and 11 .7. 3. From Eqs. (11.4.4) and (11.4.15) we obtain the partial velocities and partial ... 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 constraint equa...
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Dynamics of Mechanical Systems 2009 Part 9 potx
... 11 .7 we found the generalized active forces to be (see Eqs. (11 .7. 14) to (11 .7. 17) ): (12.2.24) (12.2.25) (12.2.26) and (12.2. 27) where, as before, m is the mass of each particle, M is the mass of ... Coordinates, Constraints, and Degrees of Freedom P11.2.1: Determine the number of degrees of freedom of the following systems: a. Pair of eyeglasses b. Pair of pliers o...
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Dynamics of Mechanical Systems 2009 Part 10 pot
... as: (13 .7. 9) By substituting from Eq. (13 .7. 7) into (13 .7. 4) we have: (13 .7. 10) or (13 .7. 11) That is, (13 .7. 12) Equation (13 .7. 12) is equivalent to the scalar equations: (13 .7. 13) (13 .7. 14) (13 .7. 15) As ... analysis for the eigenvalue problem of Sections 7. 7, 7. 8, and 7. 9. Indeed, a comparison of Eqs. (13 .7. 13), (13 .7. 14) and (13 .7. 15) with Eq. (7. 7.10), s...
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