ar X iv : m at h - ph / 0 60 80 60 v 1 2 8 A ug 2 00 6 Kinematic geometry of triangles and the study of the three - body problem
نویسنده
چکیده
2 The basic setting and a presentation of the Main Theorems 8 2.1 Basic notions and terminology . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Vector algebra and kinematics in the Euclidean space M0 9 2.1.2 Oriented m-triangles and their configuration space M . . 10 2.1.3 Congruence moduli space and shape space . . . . . . . . . 11 2.2 Statement of the Main Theorems . . . . . . . . . . . . . . . . . . 12 2.2.1 Kinematic geometry of m-triangles and universal sphericality 12 2.2.2 Unique lifting property . . . . . . . . . . . . . . . . . . . 13 2.2.3 Angular velocities and kinematic Gauss-Bonnet formula . 14 2.2.4 Moving eigenframe and Euler equations for m-triangles . 15 2.2.5 The reduced Newton’s equations . . . . . . . . . . . . . . 17 2.2.6 Reduction of the least action principles . . . . . . . . . . 18 2.2.7 Shape curves of triple collision trajectories . . . . . . . . . 19
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تاریخ انتشار 2006