caa a22 4500 467987297 CHVBK 20180323112535.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF00051045 doi (NATIONALLICENCE)springer-10.1007/BF00051045 Vivarelli Maria Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italia aut On the connection among three classical mechanical problems via the hypercomplex KS-transformation [Elektronische Daten] [Maria Vivarelli] With reference to our previous notes [23-30] on the hypercomplex regularizations of the classical Kepler problem and on the hypercomplex descriptions of the classical rotational mechanics, we arrive at an intimate mathematical relationship among the three classical mechanical problems: the elliptic Kepler problem, the spherical Euler-Poinsot problem and the four-dimensional isotropic harmonic oscillator. A key role is played: (i) by the Kustaanheimo-Stiefel (KS) regularizing transformation viewed, in the light of Souriau's quantization procedure, as the projection map in the Hopf fibering of the contact 3-sphere; (ii) by a novel Lagrangian description of rotational kinematics expressed in terms of the Euler-Rodrigues parameters; (iii) by the unit vector a (characterizing both the attitude frame of the rotator and the direction of the major axis of the Kepler orbit) and shown to link ‘à la Cartan' the KS-theory with the rotation theory. The Kepler-Poinsot-Oscillator connection is examined also in a quantistic Schroedinger approach and is related to the results of Ikeda and Miyachi. Kluwer Academic Publishers, 1991 KS-transformation nationallicence regularization nationallicence two body problem nationallicence Euler-Poinsot problem nationallicence Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/2(1990-06-01), 109-124 0923-2958 50:2<109 1990 50 10569 https://doi.org/10.1007/BF00051045 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00051045 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vivarelli Maria Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italia aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/2(1990-06-01), 109-124 0923-2958 50:2<109 1990 50 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer