Advanced Engineering Dynamics 2010 Part 14 ppsx

... (9.138) (9.139) (9 .140 ) So, summing for a group of particles and using equation (9.134) we obtain 1 l2 6s = -J- sr = 0 JC t, or simply 12 ti t2 tl 6J-r =o (9 .141 ) This suggests ... is (A1 .14) c = (A)~(B) (A1 . 1 5) and this is the scalar product. Appendix 1 Vectors, Tensors and Matrices Cartesian co-ordinates in three dimensions In our study of...

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... Advanced Engineering Dynamics H. R. Harrison Formerly Department of Mechanical Engineering & Aeronautics City University London T. Nettleton Formerly Department of Mechanical Engineering ... dynamics or hydrodynamics or aerodynamics and is not covered in this book. The object of this book is to form a bridge between elementary dynamics and advanced special...

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... a group of particles 15 1.13 Newton's laws for a group of particles Consider a group of n particles, three of which are shown in Fig. 1.1 1, where the ith parti- cle has ... on the particle is the vector sum of the forces due to each other particle in the group and the resultant of the external forces. If & is the force on particle i due to particle ......

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... then the time integral will be integrated by Parts because 6u = 0 at t, and t2. The second term in equation (3.18) is Integrating by parts gives (3.19) 50 Hamilton S principle ... integrating by parts, h 6x 1; - It:mi 6x dt - kx 6x dt = 0 4 (3.10) Rotating fiame of reference and velocity-dependent potentials 37 It is interesting to note that for a charged par...

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... bring the body into the desired position. It is worth noting that if the displacement of all particles is planar such that the rotation axis is normal to that plane then any change in position ... x m,i; (4.9) (4.10) From Fig. 4.5 r~ = rA + PI where p, is the position vector of particle i relative to A. For a rigid body equation (4.7) gives (4.11) r; = VA + 0, x ....

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... air or in space. The pur- pose of the chapter is to bring out some of the characteristic dynamics in the particular domain. Satellite motion is typified by the motion of a small body about a large ... fact that torques do not just produce angular accelerations in a straightforward analogy with particle dynamics seems to require reconciliation. A simple example will serve to illustra...

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... satellite's orientation to oscillate. We first consider a general group of particles, as shown in Fig. 5 .14, and use equation (5.3) to find the gravitational potential at point P. From ... conditions when o = oo. Thus 1 12 Dynamics of vehicles (5.96) 1 2 where C, is the drag coeficient. The drag coefficient is the sum of two parts, the first being the s...

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... behaves as an elastic spring with linear or non-linear characteristics. Referring to Fig. 6 .14 we see that the impacting surfaces are convex and the separation of the two reference planes ... c,g' - CJ (6.44) and the contact force X = -(EA),g' = +(EA)# (6.45) Fig. 6 .14 Dispersive waves 15 1 where the suffix 0 refers to a mean value and A signifies the...

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... or in matrix form where p -1lR 0 OOP and d' p'ds (6 .140 ) (6 .141 ) (6 .142 ) (6 .143 ) (6 .144 ) (6 .145 ) A cross-section has a displacement u and a rotation 0 from its ... u,lR - 0k &k = puk + 0j These are related to the elastic constants by (6 .147 ) (6 .148 ) (6 .149 ) (6.150) ... that av 60 = 6 ( dx) (6.107) (6.108) (6.109...

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... shall only be con- cerned with the overall dynamics and not with the detail. This is a vast subject area of which dynamics is a substantial and vital part. 8.2 Typical arrangements 8.2.1 CARTESIAN ... SUCCESSIVE ROTATIONS ABOUT FIXED AXES 8 Robot Arm Dynamics 8.1 Introduction In this chapter we examine the way in which three-dimensional dynamics is applied to a sys-...

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