Abstract
We review the Levi-Civita, Kustaanheimo-Stiefel and radial-inversion regularizing transformations. The Levi-Civita technique is used to deal with planar motions and its extension to the spatial case is the Kustaanheimo-Stiefel transformation. An alternative procedure is provided by the so-called radial-inversion transformation. In all cases, the basic tool is to perform suitable coordinate and time transformations in the extended phase space. We apply the Levi-Civita, Kustaanheimo-Stiefel and radial-inversion transformations to the two-body problem and to the restricted three-body problem. The Hamiltonian formalism is used, which ensures the canonicity of the transformations.
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© 2002 Springer-Verlag Berlin Heidelberg
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Celletti, A. (2002). The Levi-Civita, KS and Radial-Inversion Regularizing Transformations. In: Benest, D., Froeschlé, C. (eds) Singularities in Gravitational Systems. Lecture Notes in Physics, vol 590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48009-9_2
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DOI: https://doi.org/10.1007/3-540-48009-9_2
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