Comparison with Hills equations s Two doF Linearized Pendulum equations 2=sin corcos po gsin r 213 r cos ncos o 0 sIn y Evaluated at =649 01.8n66-42n20| where n= COS 6L-2.2n086 0060 8 Two DOF Linearized Hills Equations 02n 3n20x ssL-2n oslo oyComparison with Hill’s Equations Comparison with Hill’s Equations F Two DOF Linearized Pendulum Equations: F Evaluated at = 64 o F Two DOF Linearized Hill’s Equations: φo δ śφ ś δ śθ ś ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ = 0 2 g r sin φ o cos φ o − 2 g r cos φ o sin φ o 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ δφ ś δθ ś ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ + − g r sin 2 φ o cos φ o 0 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ δφδθ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ δφ śś δθ śś ⎧⎨ ⎩ ⎫⎬ ⎭ = 0 1.8 n −2.2n 0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ δ φś δθ ś ⎧⎨ ⎩ ⎫⎬ ⎭ + −4.2n 2 0 0 0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ δφδθ ⎧⎨ ⎩ ⎫⎬ ⎭ where n = g r cos φ o x śś y śś ⎧⎨ ⎩ ⎫⎬ ⎭ = 0 2 n −2n 0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ x śy ś ⎧⎨ ⎩ ⎫⎬ ⎭ + 3n 2 0 0 0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ x y ⎧⎨ ⎩ ⎫ ⎬ ⎭