04040nam 22006975 450 991025458140332120200706115918.03-319-52899-810.1007/978-3-319-52899-1(CKB)3710000001364446(DE-He213)978-3-319-52899-1(MiAaPQ)EBC4858108(PPN)201471620(EXLCZ)99371000000136444620170512d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe Three-Body Problem and the Equations of Dynamics Poincaré’s Foundational Work on Dynamical Systems Theory /by Henri Poincaré1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XXII, 248 p. 9 illus.)Astrophysics and Space Science Library,0067-0057 ;4433-319-52898-X Includes bibliographical references and indexes.Translator's Preface -- Author's Preface -- Part I. Review -- Chapter 1 General Properties of the Differential Equations -- Chapter 2 Theory of Integral Invariants -- Chapter 3 Theory of Periodic Solutions -- Part II. Equations of Dynamics and the N-Body Problem -- Chapter 4 Study of the Case with Only Two Degrees of Freedom -- Chapter 5 Study of the Asymptotic Surfaces -- Chapter 6 Various Results -- Chapter 7 Attempts at Generalization -- Erratum. References -- Index. .Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits.  Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. .Astrophysics and Space Science Library,0067-0057 ;443DynamicsErgodic theoryStatistical physicsAstrophysicsPhysicsPlanetary scienceDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XStatistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Astrophysics and Astroparticleshttps://scigraph.springernature.com/ontologies/product-market-codes/P22022History and Philosophical Foundations of Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P29000Planetary Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/P22060Dynamics.Ergodic theory.Statistical physics.Astrophysics.Physics.Planetary science.Dynamical Systems and Ergodic Theory.Statistical Physics and Dynamical Systems.Astrophysics and Astroparticles.History and Philosophical Foundations of Physics.Planetary Sciences.510Poincaré Henriauthttp://id.loc.gov/vocabulary/relators/aut416664MiAaPQMiAaPQMiAaPQBOOK9910254581403321The Three-Body Problem and the Equations of Dynamics2004699UNINA