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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... 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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... 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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