caa a22 4500 445863250 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10569-011-9381-z doi (NATIONALLICENCE)springer-10.1007/s10569-011-9381-z Salehani Mahdi Department of Mathematical Sciences, NTNU, 7491, Trondheim, Norway aut Global geometry of non-planar 3-body motions [Elektronische Daten] [Mahdi Salehani] The aim of this paper is to study the global geometry of non-planar 3-body motions in the realms of equivariant Differential Geometry and Geometric Mechanics. This work was intended as an attempt at bringing together these two areas, in which geometric methods play the major role, in the study of the 3-body problem. It is shown that the Euler equations of a three-body system with non-planar motion introduce non-holonomic constraints into the Lagrangian formulation of mechanics. Applying the method of undetermined Lagrange multipliers to study the dynamics of three-body motions reduced to the level of moduli space $${\bar{M}}$$ subject to the non-holonomic constraints yields the generalized Euler-Lagrange equations of non-planar three-body motions in $${\bar{M}}$$ . As an application of the derived dynamical equations in the level of $${\bar{M}}$$ , we completely settle the question posed by A. Wintner in his book [The analytical foundations of Celestial Mechanics, Sections 394-396, 435 and 436. Princeton University Press (1941)] on classifying the constant inclination solutions of the three-body problem. Springer Science+Business Media B.V., 2011 Three-body problem nationallicence Kinematic geometry nationallicence Non-holonomic mechanical systems nationallicence Generalized Euler-Lagrange equations nationallicence Constant inclination solutions nationallicence Celestial Mechanics and Dynamical Astronomy Springer Netherlands 111/4(2011-12-01), 465-479 0923-2958 111:4<465 2011 111 10569 https://doi.org/10.1007/s10569-011-9381-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9381-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Salehani Mahdi Department of Mathematical Sciences, NTNU, 7491, Trondheim, Norway aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 111/4(2011-12-01), 465-479 0923-2958 111:4<465 2011 111 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer