Abstract
We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form ∂T/∂A=−∂Φ/∂E, whereT is the period,A is the angular momentum, Φ is the angle through which the system has rotated after one period, andE is the energy.
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Hénon, M. A relation in families of periodic solutions. Celestial Mechanics 15, 99–105 (1977). https://doi.org/10.1007/BF01229050
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DOI: https://doi.org/10.1007/BF01229050