## The Libration of a Satellite |

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action actual aline angle angular velocity approximate artificial assignment axes axis binormal cause center of mass centrifugal forces circular orbit coincides complete components condition 30 condition of stability connected consider consideration constant coordinates definite determined direction cosines disregarding dumbbell elliptical equation equation 22 equations of motion exact example existence figure follows given gravitational inertial ellipsoid initial integrals intermediate axis introduce known largest axis Liapunov libration lines of force moment moments moon moves mutually necessary Newtonian force field normal occurs oscillations particular period perturbations pitch plane position position of relative possible potential function principal problem radius vector reference region relations relative equilibrium remaining restoring result rotation satellite satisfied shown shows small with respect solid body solution stability of relative stationary sufficient conditions tend theory tion unperturbed motion unstable value eq