Abstract
Lambert and Watson (1976) examine the family of symmetric linear multistep methods for the special second-order initial value problem, and connect the property of symmetry with a property of periodicity. The problems of celestial mechanics may be formulated as second-order initial value problems, but these frequently incorporate the first derivative explicity. It is common for such equations to be reduced to a system of first-order equations. Thus motivated, we utilize ideas from the aforementioned paper to determine the family of linear multistep methods for first-order initial value problems that possess an analogous property of periodicity. This family of orbitally stable methods is illustrated by examining the regularized equations of motion of an artificial earth satellite in an oblate atmosphere.
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Moore, P. Orbitally stable multistep methods. Celestial Mechanics 17, 281–297 (1978). https://doi.org/10.1007/BF01232833
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DOI: https://doi.org/10.1007/BF01232833