State transition matrix, motion constants, and ergodicity of the Euler-Poinsot problem
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2016, Springer Science+Business Media Dordrecht. This paper complements some of the classic presentations of EulerPoinsot motion in three ways. First, the state transition matrix for the attitude relative to an arbitrary inertial frame is presented. The state transition matrix elements are shown to be functions of common elliptic, circular, or hyperbolic functions of time depending on the motion state. Second, a complete set of global, time-independent integrals, here referred to as motion constants, are presented. The motion constants are functions involving the systems momentum and attitude states, and they are valid for any set of attitude coordinates. Third, conditions for the ergodic or periodic nature of the motion are derived. These conditions correspond to one of the motion constants being nonisolating.