Hills equations 8 Governing equations where 'n' is orbital frequency in rad/sec s0-2n0|-3n200 箩}+2n00y+000 00000n a accelerations account for non-central forces(drag, thrust, etc. x-axis in zenith, y-axis in frame's velocity and z-axis in transverse di erections o Free orbit solution where Aand B are lengths anda ar phase angles X= Acos(nt+a) y=-2A Sin(nt +a)-(3/2)nxt+y Z=Bcos(nt+β)Hill’s Equations Hill’s Equations F Governing equations where ‘n’ is orbital frequency in rad/sec: — accelerations account for non-central forces (drag, thrust, etc.). — x-axis in zenith, y-axis in frame’s velocity, and z-axis in transverse directions. F Free orbit solution where ‘A’ and ‘B’ are lengths and ‘α’ and ‘β’ are phase angles. x śś y śś śz ś ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ + 0 −2n 0 2n 0 0 0 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤⎦ ⎥ ⎥ ⎥ x śy śz ś ⎧⎨ ⎪ ⎩ ⎪ ⎫⎬ ⎪ ⎭ ⎪ + −3n2 0 0 0 0 0 0 0 n2 ⎡⎣ ⎢ ⎢ ⎢ ⎤⎦ ⎥ ⎥ ⎥ xyz⎧⎨ ⎪ ⎩ ⎪ ⎫⎬ ⎪ ⎭ ⎪ = ax ay az ⎧⎨ ⎪ ⎩ ⎪ ⎫ ⎬⎪ ⎭⎪ x = Acos(nt + α) + xo y = −2Asin(nt + α) −(3/ 2)nxot + yo z = Bcos(nt + β)