Derive the 6-degree of freedom equation of motion.

= X = Y = Z m[ vr + wq xg(q2 + r2) + y;(pq i) + zg(pr+q)] m[v wp + ur yg(r2 + p2) + zg(qr p) + xg(qp + r)] m[w uq + vp zg(p2 +q) + xg(rp ) + yg(rq + p)] IxP + (I. Iy)qr (r + pq)Ixz + (p2 q2)1yz + (pr )Ixy + m[yg(w uq + vp) zg(j wp + ur)] Iy + (1x Iz)rp (p + qr)Ixy + (p2 r2)/2x + (qp i')Iyz + m[zg( vr + wq) xg(w uq + vp)] I-' + (1y Ix)pq - (q + rp)Iyz + (q? p2)Ixy + (rq - P)Izx + m[xg(v wp + ur) yg( vr + wq)] = K = M = N = X = Y = Z m[ vr + wq xg(q2 + r2) + y;(pq i) + zg(pr+q)] m[v wp + ur yg(r2 + p2) + zg(qr p) + xg(qp + r)] m[w uq + vp zg(p2 +q) + xg(rp ) + yg(rq + p)] IxP + (I. Iy)qr (r + pq)Ixz + (p2 q2)1yz + (pr )Ixy + m[yg(w uq + vp) zg(j wp + ur)] Iy + (1x Iz)rp (p + qr)Ixy + (p2 r2)/2x + (qp i')Iyz + m[zg( vr + wq) xg(w uq + vp)] I-' + (1y Ix)pq - (q + rp)Iyz + (q? p2)Ixy + (rq - P)Izx + m[xg(v wp + ur) yg( vr + wq)] = K = M = N