Advanced Engineering Dynamics 2010 Part 2 doc

... to m,x, + k,x1 - k2(x2 - XI) + c,X, - ~2( X2 - XI) = F, and for x, mg2 + k2(x2 - xI) + c2(X2 - X,) = F2 Fig. 2. 2 Energv for a group of particles 17 1.14 Conservation ... the system shown in Fig. 2. 2 the scalar functions are k, 2 k2 Y = -XI + -(x2 - XJ2 2 2 Ci -2 C2 2 2 3 = -XI + -(X2 - X,f The virtual work done by the ext...

Ngày tải lên: 10/08/2014, 20:20

... Thus e.1.e = l2d + m2z2 + n2z3 = (1 - n2)1, + n2z3 Finally equation (5.59) is Gm G [3(1 - n2>1, + 3n24 - 2~ , - z,] p= +- R 2~ 3 R 2~ 3 G (3n2 - I)(z, - 1,) ... Let r = tan(W2) so that 2r 1 + T2 sin0 = and Substituting into equation 5.48 gives J(1 - e32r (1 + r*) + e(l - r2) sin0 = 2 tan(0 /2) 1 + tan2(0 /2) sin0 = C...

Ngày tải lên: 10/08/2014, 20:20

... below V [ - !! (4 + 2e-”) z + 2 (f rz2 + B2 ] L f2 = - C where and (2 - 4p) + 3 12 f3 = - e-’LL’L - - 2p [ -4p+ c [Le (6.81) (6. 82) where B, = e-6p + ... or c2 = Elp as before. Fig. 6. 12 148 Impact and one-dimensional wave propagation Fig. 6 .21 Fig. 6 .22 Maximum strain at x = L for various period numbers, n 1 2 1...

Ngày tải lên: 10/08/2014, 20:20

... = y2m[y2(a)T(u)u,/c2 + a,] F, = y2m[y2(a)T(u)uy/c 2 + 4 = y2rn[y2(alT(u)u,/c2 + aZ] (9.1 12) (9.1 13) (9.1 14) (9.115) (9.1 16) (9.1 17) (9.118) The Doppler effect 24 5 ... YXI > lx - .VI (1 - yx)’ > (x - y )2 1 + y2x2 - 2yx > x2 + y2 - 2yx (1 - x’) > y2(1 - x2) 1 >y2 or Finally which satisfies our conditions. Beca...

Ngày tải lên: 10/08/2014, 20:20

... 63 1 72 1 72 1 72 176 177 178 179 184 186 189 1 92 194 194 194 197 22 3 23 5 23 5 23 5 24 0 24 1 24 2 24 6 24 9 25 0 25 2 25 4 25 6 25 8 26 1 27 2 28 1 28 8 Bibliography 29 7 Index ... particles The principle of virtual work D’Alembert’s principle 2 Lagrange’s Equations 2. 1 2. 2 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 2. 10 2. 1 1 Introd...

Ngày tải lên: 10/08/2014, 20:20

... The kinetic energy is given by m .2 m -2 I .2 I .2 2 2 2 2 The virtual work done by the impact force at A is T = -XI + -x2 + -e, + -e2 6W = F(-dr, + ado,) and the ... - o,o,z] + 2m(w,i - or$) -efv = m[(q + o,)y - o,.o,z - o,o,x] + 2m(o$ - oj) or Similarly 2 2 2 2 2 -efz = m[(o, + O,)Z - O,O,X - O,O,,y] + 2m(ox9...

Ngày tải lên: 10/08/2014, 20:20

... f = 21 ,xi + 2Z2yj + 21 ,zk Now x=lp=- ZO = - Ox gradf = - 2L \ (2T) \ (2T) etc., so \ (2T) Kinetics of a rigid body 59 (4.5) (4-6) ds = del X a + de2 X (a ... rotation is about the z axis equation (4.43) reduces to 1 2 T = - ~rn,(a~xj - w,yi )2 1 2 = - a2Cmi(x2 + y2) 12 =-a I, 2 (4.47) (4.48) Since the choice of axis...

Ngày tải lên: 10/08/2014, 20:20

... _- P m, m2 2 2 IF,^^ = m,w r, - mI?, = m2m r, - m2r2 and taking moments about the centre of mass (C of M) gives 0 = m,(r,& + 2wi,) = m2(r2& + 2wi2) or (5.15) ... P,cos~ )2 P: E = - Z,e2 + + - + mgh cos8 (4.89) 2 21, sin2 0 21 3 Equation (4.89) can be rearranged in the following form 1 2 E’ = - z,e2 + v (e) where the c...

Ngày tải lên: 10/08/2014, 20:20

... dx - 0) = -V2 2 (6. 122 ) (6. 123 ) (6. 124 ) (6. 125 ) It is now possible to eliminate 0 between equations (6. 120 ) and (6. 12 1). Equation (6. 120 ) can be written as 2 2 V.lf - KC, ... + dzk 1 62 Impact and one-dimensional wave propagation we get 2 2 COS (k) - 2 = - - mw S or 2 2( -2 sin2 (W2)) = - = S giving o = 21 (s/m) sin(W2)...

Ngày tải lên: 10/08/2014, 20:20

... terms of their components Pzr = Plr + 4 P2, = PI, + 4 P 22 = PI; 4- u: or (Pz) = (PI) + (4 (8 .22 ) Kinematics of a robot arm 2 13 Fig. 8.19 ce, o se, a,ce, 3[A]4 ... O)T, a null vector), we may now combine equations (8 .23 ) and (8 .24 ) to give (8 .25 ) or, in abbreviated form, (P2) = [Tl(dl) (8 .26 ) Here (3) is the 4 X 1 homogeneous...

Ngày tải lên: 10/08/2014, 20:20