Abstract
The nondeterministic nature of celestial mechanics is discussed and its relation to stability investigations is treated. Uncertainties in the initial conditions, unknown dynamical effects and nonintegrability, when combined with the inherent instability of the dynamical system result in indeterminism. As consequences, ensembles of trajectories take the place of single trajectories and reliable long-time predictions become unrealistic expectations. Deterministic problems become class-room exercises, utilizing classical or mathematical models of dynamics. At the same time all real problems are shown to be nondeterministic and Laplace’s demon is exercised. This paper first defines the concepts to be used, lists reasons for indeterminism and offers several examples. This is followed by a discussion of stability as related to determinism. The role of uncertainties and important time scales are treated next. The existence of integrals and transformations of dynamical systems are shown to be beneficial to determinism but in fact they only delay the built in catastrophic trends.
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© 1986 D. Reidel Publishing Company
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Szebehely, V. (1986). New Nondeterministic Celestial Mechanics. In: Bhatnagar, K.B. (eds) Space Dynamics and Celestial Mechanics. Astrophysics and Space Science Library, vol 127. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4732-0_1
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DOI: https://doi.org/10.1007/978-94-009-4732-0_1
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