Navier-Cauchy equations : ( + G)V( ) + GV = 0where , G are constant (1)...

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Navier-Cauchy equations : ( + G)V( ) + GV = 0where , G are constant (1) Please express Navier-Cauchy equations in index notation for Cartesian coordinate (2) Please write down equations in conventional notation for two dimensional Cartesian coordinate, u1(x1,x2) If u(r, 0) (3) If u(r, 0) = = (4) If u(r, 0) = + U2 (x1,x2)2. ur(r,0) +u(r, 0), Please derive equations for two-dimensional polar coordinate. uz (r, 0)z, Please derive equations for cylindrical coordinate. Navier-Cauchy equations : ( + G)V( ) + GV = 0where , G are constant (1) Please express Navier-Cauchy equations in index notation for Cartesian coordinate (2) Please write down equations in conventional notation for two dimensional Cartesian coordinate, u1(x1,x2) If u(r, 0) (3) If u(r, 0) = = (4) If u(r, 0) = + U2 (x1,x2)2. ur(r,0) +u(r, 0), Please derive equations for two-dimensional polar coordinate. uz (r, 0)z, Please derive equations for cylindrical coordinate.