×

The Levi-Civita time transformation and a Killing vector for the Kepler problem. (English) Zbl 0874.70009

Summary: As an outcome of the hypercomplex unitary description of some aspects of the Kepler problem (regularization and prequantization of the Kepler manifold), we show how both the differential time transformation adopted by Levi-Civita for the regularization of the plane problem, and the quaternionic transformation which prequantizes the Kepler manifold, can be derived from the same quaternionic definition of a Keplerian orbit. Moreover, we show how the stereographic projection of an hodographical sphere leads to a Killing vector, the counterpart of the position vector of the particle.

MSC:

70F05 Two-body problems
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
PDFBibTeX XMLCite
Full Text: DOI