Download Complate Issue - Ozean Publications

Ozean Journal of Applied Sciences 2(2), 2009Now, starting from equation (15.1) and adding at the same time, subtracting the termd(mvdtor,or,zd(mvdt⎛⎜)= m⎜⎜a⎜⎝zz+c⎡⎛⎢⎜)= m⎢⎜⎢⎜a⎢⎜⎣⎝zuvzaxuv⎛⎜ −⎝2 1+ccx2⎛⎜ −⎝2 1⎞⎟⎟⎞ ⎟⎟ ⎟⎠ ⎠uvzaxuvc+x2⎛⎜⎜m⎜⎜c⎝⎞⎟⎟⎞ ⎟⎟ ⎟⎠ ⎠+vzav uvzax−2⎛ v ⎞ 2 ⎛ uv⎜1− ⎟ c ⎜2 −2⎝ c ⎠ ⎝ c2 1⎛⎜⎜ vz( a⎜⎜⎝xvx+ ayvy+ azv2⎛ v ⎞c⎜1− ⎟2⎝ c ⎠x⎞⎟⎟⎟⎞⎟ ⎟⎠⎠)−c2 21zuvzax⎛ uv⎜ −2⎝ cuvzax2 uvxc ( 1−)2c⎡⎛⎞⎢⎜⎟d(mvz) ⎢⎜uvzax⎟ vzax( vx− u)vzvy= m⎢⎜az++dt⎛ uv ⎞ ⎟+ ( +⎢⎜c2 ⎜1−x ⎛ ⎞ ⎛ ⎞⎟ ⎟2 ⎜ ⎟⎣⎝⎝ c ⎠⎜ −⎟⎜ −⎟⎠⎠⎛ ⎞a22 y2 uv −x v 2 vc 1 1 c 1222⎝ c ⎝ c ⎠ ⎝ c ⎠⎞⎛⎞⎤⎟⎜⎟2⎥uvyax⎟ vz⎟+⎜ uvzax⎟⎥2 ⎛ ⎞⎜ − 2⎟ ⎟⎝1 uv⎜a +2 z⎟⎥x2⎛ v ⎞2 ⎛ uv ⎞c⎜ ⎜ −xc⎟ ⎟⎥c ⎠⎜1− ⎟ c 122⎠ ⎝ c ⎠ ⎝ ⎝ c ⎠ ⎠⎥⎦1, we obtain⎛ uv ⎞ γ ⎜1− x2⎟⎝ c ⎠Now if we take equation (16) and multiplying, at the same time, dividing it byFz⎡ ⎛⎞⎢ ⎜⎟⎞ ⎢ ⎜⎟⎜⎛ uv − x 1uvzaxvzax( vx− u)γ 1 ⎟m⎢ ⎜a +2z⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎟+ +c uv⎢ ⎜ −x2 uv1 ⎟ ⎜ c ⎜1−xγ⎟ ⎟⎞ ⎛ ⎞2⎜⎛ 2 22 uv − x vc γ 1 ⎟⎣ ⎝ c ⎠ ⎝ ⎝ c ⎠ ⎠⎜1−⎟22⎝ c ⎠ ⎝ c ⎠=2x⎞⎤⎟⎥⎟⎥⎟⎞ ⎥⎟ ⎟⎥⎠⎠⎥⎦, then we have(16)⎛⎞⎜⎟2vzvy ⎜ uvyax⎟ vz⎜+⎟+⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜⎜⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎟ ⎜ −⎟⎠⎛ ⎞⎟ −−−⎠⎛ ⎞a2 y22 uv2 uv−x vx 2 uvxvc γ 1 1c 1222c γ 1 122⎝ c ⎝ c ⎠ ⎝ ⎝ c ⎠ ⎠ ⎝ c ⎝ c ⎠⎛⎜⎜⎜a⎜⎝z+cuvzaxuv⎛⎜ −⎝2 1cx2⎞⎤⎟⎟⎞ ⎟⎟ ⎟⎥ ⎥⎥⎥ ⎠ ⎠⎦Now substituting the above result in equation (13), we obtain235