Advanced Engineering Dynamics 2010 Part 8 docx

... + 312 f3 = - e-’LL’L - - 2p [ -4p+ c [Le (6 .81 ) (6 .82 ) where B, = e-6p + e-4’ (1 - 8p) + e-’’’ (1 - 8p + 8p’) + 1 At the impact point, x = 0, the velocity ... but this time versus x. An increase of 21.r in the argument cor- kh = 2n (6 .88 ) or k = 2dh (6 .89 ) k is known as the wavenumber. Fig. 6.24 I 36 Impact and one-dimensio...

Ngày tải lên: 10/08/2014, 20:20

... of momentum relative to the centre of mass is L, = Api + Bqj + Crk (5 .84 ) (5 .85 ) (5 .86 ) 100 Dynamics of vehicles c = -1 1" dr = (d2 + r3/6)- 1" YK 241 ... - APdk (5 .87 ) The moment of forces about G is MG = Li + Mj + Nk Therefore (5 .88 ) L, = Ap + (C - B)qr M = Bq + (A - C)rq N = Ci + (B - A)pq (5 .89 ) (5...

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... frames. From equation (9 .83 ) we get (9 .83 ) (9 .84 ) (9 .85 ) (9 .86 ) Thus from equation (9 .84 ) ux - v u,’ = (1 - vu,/cz) and from equations (9 .85 ) and (9 .86 ) uz u: = (1 - vu,/cz) ... x: (9 .88 ) (9 .89 ) (9.90) (9.9 1) If the length of the outward journey is L then when x = L, x’ = 0, so from equation t,“ and x{ are constants to be d...

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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 ... termed To and is the kinetic energy of a single particle of mass m located at the centre of mass. The second term will be J 2 J Fig. 2 .8 Ha m i It o n’s Pr i nci p I e 3.1 ....

Ngày tải lên: 10/08/2014, 20:20

... wavenumber K= Rk and the non-dimensional frequency (6. 182 ) (6. 183 ) (6. 184 ) 1 66 Impact and one-dimensional wave propagation Fig. 6 38 or U,l (PI = PAD2@) (6.161) The component equations ... along the axis of the wire. Thus (6.1 78) 0, = 0, e (6.179) 01- J up = GkeJ("'-k') (6. 180 ) p"0, = R (-Jk)0, (6. 181 ) J(0f - b) - 0&apos...

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... (ef>(e)T@> (8. 8) Now 3. 3 il.,*f 3. kl (e‘)(e’)T - - ( ’:) ( 3 jl kl ) = [ jf. il jf.jl jl. kl ] k’ k’. i’ k1.j’ k’. k’ =[; 8 B] (8. 9) so that equation (8. 8) reads ... 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 CO-ORDI...

Ngày tải lên: 10/08/2014, 20:20