Page 172 - Standard Handbook Of Petroleum & Natural Gas Engineering

Dynamics 157

d
aH = --(vH) = -LO; cosw,ti - LW; sinw,ij
dt

Assuming point B is fixed and analyzing the motion of point C with respect to B (see
Figure 2-13c),

r( = RcosO,i+RsinO,j

V, ,, = - Rw, sin w, ti + Rw, cos w, tj

a, ,, = -R~E cosw,,tl+ RW: sin w,,tj

Thus the velocity of point C is

v, = v,, + v,:,,, = -(La, sinw,t + Rw,: sinw,:t)i

+ (Lw, cosw,t + Rw,: cosw,t)j

2rev 1minI 2nr
w, = = 0.209rps
min 1 60s I revolution

w< = -0.524 rps
Rw, = -0.524 ft/S

V, = -[0.418sin(0.209t) - 0.524sin(-0.524t)]i
+ [ 0.418c0s( 0.209 t ) - 0.524 cos( -0.524 )] 3
t

At t = 0, for instance, the velocity is (see Figure 2-13d)
V, = -O.lOSjft/s

Likewise, the general expression for the acceleration of point C is

a, = a,, +a, , = -(LO; cosw,t + Ro: cosw,t)i

- (LO:, sin w,.t + RO:. sinw, t)'j
At t = 0 this reduces to

a, = -( L wi + Rw: )I = -[ 2 x 0.209' + 1 x (-0.524)*]3