Abstract
Concepts of stability, associated nomenclature and names of originators are reviewed emphasizing some global aspects as well as specific applications to dynamics and to celestial mechanics. Due to the many definitions and interpretations used, details concerning only a few fundamental concepts (Hill's, Liapunov's, Poincare's stability, etc.) are offered. Short definitions and descriptions are also given for about 50 concepts of stability in the form of a dictionary. Several of the definitions presently in use are not unique, in fact are often contradictory and/or repetitive. Furthermore, the credits given to the originators are not uniform or consistent in the literature and several cross-references seem to be necessary. The list of references given contains some fundamental works and it does not attempt to be complete. The entire length of this paper would have been easily taken up by a more detailed list of references, which list would still not have been “complete”.
In the “Introduction” some historical and fundamental aspects of stability are discussed. This is followed by the review of “Major Stability Concepts” in some detail. The “Dictionary of Stability” forms Part 3 and “Conclusions and Future Research” are in Part 4, treating generalizations of present techniques and outlining problems of fundamental importance and of inherent difficulties. Part 5 gives an abbreviated list of references.
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References The following list concentrates on the fundamental and basic reference articles in addition to recent books which the reader might find useful. Note that some of the text book references of this list are not mentioned in the present paper and they cover many aspects of stability of rather general interest.
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Szebehely, V. Review of concepts of stability. Celestial Mechanics 34, 49–64 (1984). https://doi.org/10.1007/BF01235791
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DOI: https://doi.org/10.1007/BF01235791