Dynamics of Mechanical Systems 2009 Part 7 pps
Dynamics of Mechanical Systems 2009 Part 7 pps
... 2002 2: 57 PM330 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)). Theright 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 called the power of F ... May 6, 2002 2: 57 PM310 Dynamics of Mechanical Systems The angular momentum of the plate about the seized edge after seizure is:(9.12.3)where IOQ is the moment of inertia of the plate about...
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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 Linear Momentum 2809.4 ... Methods of Analytical Dynamics, McGraw-Hill, New York, 1 970 .1.20. Paul, B., Kinematics and Dynamics of Planar Machinery, Prentice Hall, Englewood Cliffs, NJ, 1 979 .1.21. Sneck, H. J., Machine Dynamics, ...
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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 II, III, and IIII 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 RulesConsider again the definition of the second moment vector of Eq. (7. 2.1): (7. 5.1)Observe ... 33330593_C 07_ fm Page 203 Monday, May 6, 2002 2:42 PM230 Dynamics of Mechanical Systems where we have made use of Eqs. (7. 12.4) and (7. 12.5). Similarly, the second term of Eq. (7. 12.2) may be...
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Dynamics of Mechanical Systems 2009 Part 2 potx
... 2:03 PM68 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 columns of A and the number of rows of ... May 6, 2002 2:03 PM 72 Dynamics of Mechanical Systems Section 3.3 Position, Velocity, and AccelerationP3.3.1: The position vector p locating a particle P relative to a point O of a reference frameR...
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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, RωB is:(4 .7. 9)Finally, using ... 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 system is sometimes...
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Dynamics of Mechanical Systems 2009 Part 4 docx
... PM180 Dynamics of Mechanical Systems Therefore, by combining Eqs. (6 .7. 8) and (6 .7. 9), we obtain:(6 .7. 10)where the sum k1 + k2 is now the equivalent spring modulus.Observe that Eq. (6 .7. 10) ... Figure P5 .7. 1. Determinethe coordinates of the instant center C of B and the velocity of point Q of B whosecoordinates are (2, 4). Express the velocity of Q in terms of nx and ny.P5 .7. 2: A ... FIGURE 6.3.1 A mechanical system. FIGURE 6.3.2 A set of forces acting on a mechanical system. 0593_C06_fm Page 165 Monday, May 6, 2002 2:28 PM 172 Dynamics of Mechanical Systems As a second...
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Dynamics of Mechanical Systems 2009 Part 6 pdf
... Figure P7.3.3, find thefollowing 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 na and nb be the unitvectors of Problem P7.4.9. Find the following moments and products of inertia of S relativeto ... in terms of nx, ny,and nz.P7 .7. 3: Repeat Problem P7 .7. 2 if the square plate CDEF weighs 30 lb.P7 .7. 4: Repeat Problem P7 .7. 3 if the square plate CDEF weighs 10 lb.FIGURE P7 .7. 2A composite...
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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 n1, n2, and n3 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 ... 355The 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 equations. Forexample, if a particle ... will be onholonomic 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 VelocityConsider...
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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 FreedomP11.2.1: Determine the number of degrees of freedom of the following systems: a. Pair of eyeglassesb. Pair of pliers or pair of scissorsc. Child’s tricycle ... is a point at the end of a springwhich is part of a mechanical system S as depicted in Figure 11.11.4. Let S have n degreesFIGURE 11.11.3Elevation of a particle Q of a mechanical system S.FIGURE...
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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), shows that they are in essencethe same problem. ... PM454 Dynamics of Mechanical Systems Next, let ω be ω2 (that is, ). By substituting into Eqs. (13 .7. 13), (13 .7. 14), and(13 .7. 15), we obtain the equations:(13 .7. 24)(13 .7. 25)(13 .7. 26)These...
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