Abstract
To every invariant manifold (Σ) of an Hamiltonian system (H) is associated a particular solution. The trajectory is the set of points of (Σ) for which H is extremal. The time is determined by quadratures.
This is an extension of the well-known steady solution associated with an ignorable coordinate.
Levi-Civita, ‘Drei Abhandlungen über adiabatische Invariaten’, Opere Mathematische 4.
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© 1973 D. Reidel Publishing Company, Dordrecht-Holland
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Nahon, F. (1973). The Particular Solutions of Levi-Civita. In: Tapley, B.D., Szebehely, V. (eds) Recent Advances in Dynamical Astronomy. Astrophysics and Space Science Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2611-6_5
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DOI: https://doi.org/10.1007/978-94-010-2611-6_5
Publisher Name: Springer, Dordrecht
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