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001459968 001__ 1459968
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001459968 019__ $$a1369629174
001459968 020__ $$a9783031131158$$qelectronic book
001459968 020__ $$a3031131150$$qelectronic book
001459968 020__ $$z3031131142
001459968 020__ $$z9783031131141
001459968 0247_ $$a10.1007/978-3-031-13115-8$$2doi
001459968 035__ $$aSP(OCoLC)1369658052
001459968 040__ $$aEBLCP$$beng$$erda$$cEBLCP$$dGW5XE$$dYDX$$dUKAHL$$dYDX
001459968 049__ $$aISEA
001459968 050_4 $$aQB349$$b.I24 2020
001459968 08204 $$a521$$223/eng/20230214
001459968 1112_ $$aI-CELMECH Training School$$d(2020 :$$cMilan, Italy)
001459968 24510 $$aNew frontiers of celestial mechanics :$$btheory and applicaitons : I-CELMECH Training School, Milan, Italy, February 3-7 2020 /$$cGiulio Baù, Sara Di Ruzza, Rocío Isabel Páez, Tiziano Penati, Marco Sansottera, editors.
001459968 264_1 $$aCham :$$bSpringer,$$c[2022]
001459968 300__ $$a1 online resource (306 p.).
001459968 336__ $$atext$$btxt$$2rdacontent
001459968 337__ $$acomputer$$bc$$2rdamedia
001459968 338__ $$aonline resource$$bcr$$2rdacarrier
001459968 4901_ $$aSpringer Proceedings in Mathematics & Statistics ;$$vVolume 399
001459968 500__ $$a5 Lagrangian of a Rigid Body Interacting with a Point Mass
001459968 504__ $$aIncludes bibliographical references.
001459968 5050_ $$aIntro -- Preface -- Contents -- About the Editors -- Invariant KAM Tori: From Theory to Applications to Exoplanetary Systems -- 1 Introduction -- 2 Basics of KAM Theory -- 2.1 Near to the Identity Canonical Transformations by Lie Series -- 2.2 Statement(s) of KAM Theorem -- 2.3 Algorithmic Construction of the Kolmogorov Normal Form -- 2.4 On the Convergence of the Algorithm Constructing the Kolmogorov Normal Form -- 3 Construction of Invariant Elliptic Tori by a Normal Form Algorithm -- 3.1 Algorithmic Construction of the Normal Form for Elliptic Tori
001459968 5058_ $$a3.2 On the Convergence of the Algorithm Constructing the Normal Form for Elliptic Tori -- 4 Construction of Invariant KAM Tori in Exoplanetary Systems with Rather Eccentric Orbits -- 4.1 Secular Model at Order Two in the Masses -- 4.2 Semi-analytic Computations of Invariant Tori -- References -- A New Analysis of the Three-Body Problem -- 1 Overview -- 2 Euler Problem Revisited -- 3 Perihelion Librations in the Three-Body Problem -- 4 Chaos in a Binary Asteroid System -- References -- KAM Theory for Some Dissipative Systems -- 1 Introduction
001459968 5058_ $$a1.1 Consequences of the A-Posteriori Method for Conformally Symplectic Systems -- 1.2 Organization of the Paper -- 2 Conservative/Dissipative Standard Maps and Spin-Orbit Problems -- 2.1 The Conservative Standard Map -- 2.2 The Dissipative Standard Map -- 2.3 The Spin-Orbit Problems -- 3 Conformally Symplectic Systems and Diophantine Vectors -- 3.1 Discrete and Continuous Conformally Symplectic Systems -- 3.2 Diophantine Vectors for Maps and Flows -- 4 Invariant Tori and KAM Theory for Conformally Symplectic Systems -- 4.1 Invariant KAM Tori -- 4.2 Conformally Symplectic KAM Theorem
001459968 5058_ $$a4.3 A Sketch of the Proof of the KAM Theorem -- 5 Breakdown of Quasi-periodic Tori and Quasi-periodic Attractors -- 5.1 Sobolev Breakdown Criterion -- 5.2 Greene's Method, Periodic Orbits and Arnold's Tongues -- 6 Collision of Invariant Bundles of Quasi-periodic Attractors -- 7 Applications -- 7.1 Applications to the Standard Maps -- 7.2 Applications to the Spin-Orbit Problems -- References -- Tidal Effects and Rotation of Extended Bodies -- 1 Introduction -- 2 Coordinate System -- 2.1 The 3-1-3 Euler Angles -- 2.2 Unitary Quaternion -- 2.3 Special Case: Axisymmetric Body
001459968 5058_ $$a3 Generalised Velocity and Kinematic Equation -- 3.1 Kinematic Equation Satisfied by the Rotation Matrix -- 3.2 Kinematic Equation Satisfied by the 3-1-3 Euler Angles -- 3.3 Kinematic Equation Satisfied by Unitary Quaternions -- 3.4 Kinematic Equation Satisfied by a Unit Vector of the Figure Axis -- 4 Least Action Principle and Dynamical Equations -- 4.1 Parametrisation of the Tangent Space -- 4.2 Variation of the Action -- 4.3 Dynamical Equations -- 4.4 Rayleigh Dissipation Function -- 4.5 Spin Operator -- 4.6 Hamiltonian Formalism -- 4.7 Example: The Gyroscope
001459968 506__ $$aAccess limited to authorized users.
001459968 520__ $$aThis volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
001459968 588__ $$aDescription based on online resource; title from digital title page (viewed on March 20, 2023).
001459968 650_0 $$aCelestial mechanics$$vCongresses.
001459968 655_0 $$aElectronic books.
001459968 7001_ $$aBaù, Giulio,$$eeditor.
001459968 7001_ $$aDi Ruzza, Sara,$$eeditor.
001459968 7001_ $$aPáez, Rocío Isabel,$$eeditor.
001459968 7001_ $$aPenati, Tiziano,$$eeditor.
001459968 7001_ $$aSansottera, Marco,$$eeditor.
001459968 77608 $$iPrint version:$$aBaù, Giulio$$tNew Frontiers of Celestial Mechanics: Theory and Applications$$dCham : Springer International Publishing AG,c2023$$z9783031131141
001459968 830_0 $$aSpringer proceedings in mathematics & statistics ;$$vv. 399.
001459968 852__ $$bebk
001459968 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-13115-8$$zOnline Access$$91397441.1
001459968 909CO $$ooai:library.usi.edu:1459968$$pGLOBAL_SET
001459968 980__ $$aBIB
001459968 980__ $$aEBOOK
001459968 982__ $$aEbook
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