Perturbed Pendulum motion s Perturb motion about a nominal elevation angle and azimuthal angular rate φ=p。+8,=8。+8月 whereφ。,。= const y Substitute into nonlinear equations and zero higher order terms φ6-62(cos2。-sin2。)-scos。F6-26sind。cos6 r (。cos。-=)sin。 δ{+2 COS δF=0 sIn 8 Notice that forcing term zeroes about equilibrium motion cOSΦ、rPerturbed Pendulum Motion Perturbed Pendulum Motion F Perturb motion about a nominal elevation angle and azimuthal angular rate: F Substitute into nonlinear equations and zero higher order terms: F Notice that forcing term zeroes about equilibrium motion: φ = φ o + δ φ , θś = θś o + δ θś where φ o,θś o = const [ ]φ : δ śφ ś − [θ ś o 2(cos 2 φ o − sin 2 φ o ) − g r cos φ o ]δφ − 2θ ś o sin φ o cos φ o δθ ś = (θ ś o 2 cos φ o − g r )sin φ o [ ]θ : δ śθ ś + 2θ ś o cos φ o sin φ o δφ ś = 0 θ ś o 2 = 1 cos φ o g r