UID:
almafu_9960117449702883
Format:
1 online resource (xv, 223 pages) :
,
digital, PDF file(s).
ISBN:
1-316-54525-3
,
1-316-54756-6
,
1-316-41048-X
Series Statement:
London Mathematical Society student texts ; 83
Content:
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Note:
Title from publisher's bibliographic system (viewed on 08 Mar 2016).
,
Cover -- Series information -- Title page -- Copyright information -- Dedication -- Talbe of contents -- Preface -- The contents of this book -- Notational conventions -- Physical background -- Mathematical background -- Permissions -- Acknowledgements -- 1 The central force problem -- 1.1 Angular momentum and Kepler's second law -- 1.2 Conservation of energy -- Notes and references -- Exercises -- 2 Conic sections -- 2.1 Ellipses -- 2.2 Hyperbolas -- 2.3 Parabolas -- 2.4 Summary -- Notes and references -- Exercises -- 3 The Kepler problem -- 3.1 Kepler's first law -- 3.2 Eccentricity and energy -- 3.3 Kepler's third law -- Notes and references -- Exercises -- 4 The dynamics of the Kepler problem -- 4.1 Anomalies and Kepler's equation -- 4.2 Solution of Kepler's equation by the cycloid -- 4.3 The parabolic case: cubic equations -- Notes and references -- Exercises -- 5 The two-body problem -- 5.1 Reduction to relative coordinates -- 5.2 Reduction to barycentric coordinates -- Exercises -- 6 The n-body problem -- 6.1 The Newton potential -- 6.2 Maximal solutions -- 6.3 The Lagrange-Jacobi identity -- 6.4 Conservation of momentum -- 6.5 Sundman's theorem on total collapse -- 6.6 Central configurations -- Notes and references -- Exercises -- 7 The three-body problem -- 7.1 Lagrange's homographic solutions -- 7.2 Euler's collinear solutions -- 7.3 The restricted three-body problem -- Notes and references -- Exercises -- 8 The differential geometry of the Kepler problem -- 8.1 Hamilton's hodograph theorem -- 8.2 Inversion and stereographic projection -- 8.3 Spherical geometry and Moser's theorem -- 8.4 Hyperbolic geometry -- 8.5 The theorem of Osipov and Belbruno -- 8.6 Projective geometry -- 8.7 Newton's vs. Hooke's law -- Notes and references -- Exercises -- 9 Hamiltonian mechanics -- 9.1 Variational principles -- 9.2 The Hamilton equations.
,
9.3 Canonical transformations -- 9.4 Equilibrium points and stability -- Notes and references -- Exercises -- 10 The topology of the Kepler problem -- 10.1 The geodesic flow on the 2-sphere -- 10.2 The Kepler problem as a Hamiltonian system -- 10.3 The group SO(3) as a manifold -- 10.4 The quaternions -- Notes and references -- Exercises -- References -- Index.
,
English
Additional Edition:
ISBN 1-107-56480-8
Additional Edition:
ISBN 1-107-12540-5
Language:
English
URL:
https://doi.org/10.1017/CBO9781316410486
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