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. Singularities in Gravitational Systems Singularities in Gravitational Systems Look Inside
Celletti, A. (2002). The Levi-Civita and KS regularizing transformations. In C.F.e. D. Benest (a cura di), Singularities in Gravitational Systems (pp. 25-48). Springer-Verlag [10.1007/3-540-48009-9_2].
The Levi-Civita and KS regularizing transformations
CELLETTI, ALESSANDRA
2002-01-01
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. Singularities in Gravitational Systems Singularities in Gravitational Systems Look InsideI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
