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Dynamics of Mechanical Systems 2009 Part 9 potx

Dynamics of Mechanical Systems 2009 Part 9 potx

Dynamics of Mechanical Systems 2009 Part 9 potx

... θ0 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 TubeFor another example illustrating the use of ... ˙x˙y˙z˙X˙Y˙Z0 593 _C11_fm Page 404 Monday, May 6, 2002 2: 59 PM402 Dynamics of Mechanical Systems 11.3. Kane, T. R., Analytical Elements of Mechanics, Vol. 1, Academic Press, New York, 195 9, p. 128.11.4. ... c n L N X θφ n 3 2 1 1 2 3 ψ0 593 _C11_fm Page 385 Monday, May 6, 2002 2: 59 PM 394 Dynamics of Mechanical Systems In the development of these generalized forces we discovered that...
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Dynamics of Mechanical Systems 2009 Part 2 potx

Dynamics of Mechanical Systems 2009 Part 2 potx

... 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 ... , δij j iVV=0 593 _C02_fm Page 38 Monday, May 6, 2002 1:46 PM76 Dynamics of Mechanical Systems Determine the velocity and acceleration of P when θ is (a) 0˚; (b) 30˚; (c) 90 ˚; and (d) 180˚.P3.8.2: ... Rddtddt==220 593 _C03_fm Page 59 Monday, May 6, 2002 2:03 PM72 Dynamics of Mechanical Systems Section 3.3 Position, Velocity, and AccelerationP3.3.1: The position vector p locating a particle P...
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Dynamics of Mechanical Systems 2009 Part 1 ppsx

Dynamics of Mechanical Systems 2009 Part 1 ppsx

... 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 9. 10 Impact: Coefficient of Restitution ... Degrees of Freedom 45013.8 Analysis and Discussion of Three-Particle Movement: Modes of Vibration 455 0 593 _ FM_fm Page 14 Tuesday, May 14, 2002 10: 19 AM 6 Dynamics of Mechanical Systems ...
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Dynamics of Mechanical Systems 2009 Part 3 pptx

Dynamics of Mechanical Systems 2009 Part 3 pptx

... form:(4 .9. 31)Let aB 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 ... sinθθθ0 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 number of degrees of freedom of a mechanical ... Figure 4 .9. 4, AB is:(4 .9. 22)Let ωωωωAB be expressed in the form:(4 .9. 23)Let VB be expressed as:(4 .9. 24)Then, by substituting from Eqs. (4 .9. 19) , (4 .9. 22), (4 .9. 23), and (4 .9. 24) we...
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Dynamics of Mechanical Systems 2009 Part 4 docx

Dynamics of Mechanical Systems 2009 Part 4 docx

... 321131144 192 −+nnMnnnO=−−160 30 16812 3ftlb0 593 _C06_fm Page 168 Monday, May 6, 2002 2:28 PM160 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 PM172 Dynamics of Mechanical Systems As a second ... ×()ααωωωω0 593 _C05_fm Page 151 Monday, May 6, 2002 2:15 PM154 Dynamics of Mechanical Systems (5.8.31)(5.8.32)(5.8.33)Observe that the velocity of O is zero, as expected, but the acceleration of O...
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Dynamics of Mechanical Systems 2009 Part 5 pps

Dynamics of Mechanical Systems 2009 Part 5 pps

... rnrrnrInIIiii××()=××()=××()==⋅=⋅===∑∑∑αααααα111ααααααα0 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 ... iiNααωωωω11IpnpaPODam=××() 0 593 _C07_fm Page 199 Monday, May 6, 2002 2:42 PM188 Dynamics of Mechanical Systems P6.2.2: See Problem P6.2.1. Find the moment of F about points O, A, and B of Figure P6.2.1.Express ... expression:(6 .9. 2)where F represents the resultant of all applied forces on a particle P having mass m andacceleration a. By comparing Eqs. (6 .9. 1) and (6 .9. 2), we have:(6 .9. 3)Equation (6 .9. 3) is often...
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Dynamics of Mechanical Systems 2009 Part 6 pdf

Dynamics of Mechanical Systems 2009 Part 6 pdf

... 0 593 _C08_fm Page 2 59 Monday, May 6, 2002 2:45 PM256 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˙cosθψφθφθnnn1230 593 _C08_fm Page 267 Monday, May 6, 2002 2:45 PM260 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 ... cm 8 cm5 kg3 kg0 593 _C08_fm Page 274 Monday, May 6, 2002 2:45 PM266 Dynamics of Mechanical Systems where a2 is the n2 component of a and T3 is the n3 component of T*; a2 may be...
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Dynamics of Mechanical Systems 2009 Part 7 pps

Dynamics of Mechanical Systems 2009 Part 7 pps

... ω0 593 _C 09_ fm Page 299 Monday, May 6, 2002 2:50 PM308 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 303Equating the expressions of Eqs. (9. 9.6) and (9. 9.7), we find to be: (9. 9.8) 9. 10 Impact: Coefficient of RestitutionThe principles of impulse and momentum ... of R. Then, from Eqs. (9. 4.8), (9. 4.12), and (9. 4.13), the angular momenta of B about O, Q,and G are: (9. 6.17) (9. 6.18) (9. 6. 19) where PG and QG locate G relative to O and Q as in Figure 9. 6.5,...
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Dynamics of Mechanical Systems 2009 Part 8 docx

Dynamics of Mechanical Systems 2009 Part 8 docx

... n0 593 _C11_fm Page 370 Monday, May 6, 2002 2: 59 PM364 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 PM362 Dynamics of Mechanical Systems fixed point O in R. Let the coordinates of P be (x, y, z), the X, Y, Z Cartesian coordinates of a point ... n˙˙rrr==andθθv˙θv˙θ˙.θ0 593 _C11_fm Page 362 Monday, May 6, 2002 2: 59 PM338 Dynamics of Mechanical Systems and the block, with the sum of the potential energy of the spring and the kinetic energy of the block...
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Dynamics of Mechanical Systems 2009 Part 10 pot

Dynamics of Mechanical Systems 2009 Part 10 pot

... −()=gClᐉθ0 593 _C13_fm Page 4 59 Monday, May 6, 2002 3:21 PM462 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))+()[]=()−+()xxkm2311222ξ0 593 _C13_fm Page 456 Monday, May 6, 2002 3:21 PM436 Dynamics of Mechanical Systems References12.1. Kane, T. R., Dynamics of nonholonomic systems, J. Appl. Mech., 28, 574, 196 1.12.2. ... some of our fundamental results in examining stability of mechanical systems. References13.1. Meirovitch, L., Elements of Vibration Analysis, McGraw-Hill, New York, 197 5.13.2. Newland, D. E., Mechanical...
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