عنوان

The restricted three-body problem and holomorphic curves /

شابک

3319722786

شابک

9783319722788

شابک اشتباه

3319722778

شابک اشتباه

9783319722771

عنوان اصلي

The restricted three-body problem and holomorphic curves /

نام عام مواد

[Book]

نام نخستين پديدآور

Urs Frauenfelder, Otto van Koert.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Birkhauser,

تاریخ نشرو بخش و غیره

[2018]

نام خاص و کميت اثر

1 online resource (381 pages)

عنوان فروست

Pathways in Mathematics

متن يادداشت

8.4 Periodic orbits of the second kind for small mass ratios

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Intro; Contents; Chapter 1 Introduction; 1.1 The Birkhoff conjecture; 1.2 The power of holomorphic curves; 1.3 Systolic inequalities and symplectic embeddings; 1.4 Beyond the Birkhoff conjecture; Chapter 2 Symplectic Geometry and Hamiltonian Mechanics; 2.1 Symplectic manifolds; 2.2 Symplectomorphisms; 2.2.1 Physical transformations; 2.2.2 The switch map; 2.2.3 Hamiltonian transformations; 2.3 Examples of Hamiltonians; 2.3.1 The free particle and the geodesic flow; 2.3.2 Stereographic projection and the geodesic flow of the round metric; 2.3.3 Mechanical Hamiltonians

متن يادداشت

2.3.4 Magnetic Hamiltonians2.3.5 Physical symmetries; 2.3.6 Normal forms; 2.4 Hamiltonian structures; 2.5 Contact forms; 2.6 Liouville domains and contact type hypersurfaces; 2.7 Real Liouville domains and real contact manifolds; Chapter 3 Symmetries; 3.1 Poisson brackets and Noether's theorem; 3.2 Hamiltonian group actions and moment maps; 3.3 Angular momentum, the spatial Kepler problem, and the Runge-Lenz vector; 3.3.1 Central force: conservation of angular momentum; 3.3.2 The Kepler problem and its integrals; 3.3.3 The Runge-Lenz vector: another integral of the Kepler problem

متن يادداشت

3.4 Completely integrable systems3.5 The planar Kepler problem; Chapter 4 Regularization of Two-Body Collisions; 4.1 Moser regularization; 4.2 The Levi-Civita regularization; 4.3 Ligon-Schaaf regularization; 4.3.1 Proof of some of the properties of the Ligon-Schaaf map; Chapter 5 The Restricted Three-Body Problem; 5.1 The restricted three-body problem in an inertial frame; 5.2 Time-dependent transformations; 5.3 The circular restricted three-body problem in a rotating frame; 5.4 The five Lagrange points; 5.5 Hill's regions; 5.6 The rotating Kepler problem

متن يادداشت

5.7 Moser regularization of the restricted three-body problem5.8 Hill's lunar problem; 5.8.1 Derivation of Hill's lunar problem; 5.8.2 Hill's lunar Hamiltonian; 5.9 Euler's problem of two fixed centers; Chapter 6 Contact Geometry and the Restricted Three-Body Problem; 6.1 A contact structure for Hill's lunar problem; 6.2 Contact connected sum; 6.2.1 Contact version; 6.3 A real contact structure for the restricted three-body problem; Chapter 7 Periodic Orbits in Hamiltonian Systems; 7.1 A short history of the research on periodic orbits; 7.2 Variational approach; 7.3 The kernel of the Hessian

متن يادداشت

7.4 Periodic orbits of the first and second kind7.5 Symmetric periodic orbits and brake orbits; 7.6 Blue sky catastrophes; 7.7 Elliptic and hyperbolic orbits; Chapter 8 Periodic Orbits in the Restricted Three-Body Problem; 8.1 Some heroes in the search for periodic orbits; 8.2 Periodic orbits in the rotating Kepler problem; 8.2.1 The shape of the orbits if; 8.2.2 The circular orbits; 8.2.3 The averaging method; 8.2.4 Periodic orbits of the second kind; 8.3 The retrograde and direct periodic orbit; 8.3.1 Low energies; 8.3.2 Birkhoff's shooting method; 8.3.3 The Birkhoff set

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.

عنوان

Restricted Three-Body Problem and Holomorphic Curves.

شماره استاندارد بين المللي کتاب و موسيقي

9783319722771

موضوع مستند نشده

Hamiltonian operator.

موضوع مستند نشده

Holomorphic functions.

موضوع مستند نشده

Three-body problem.

موضوع مستند نشده

Hamiltonian operator.

موضوع مستند نشده

Holomorphic functions.

موضوع مستند نشده

MATHEMATICS-- Calculus.

موضوع مستند نشده

MATHEMATICS-- Mathematical Analysis.

موضوع مستند نشده

Three-body problem.

موضوع مستند نشده

MAT-- 005000

موضوع مستند نشده

MAT-- 034000

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Frauenfelder, Urs

مستند نام اشخاص تاييد نشده

Koert, Otto van

تاريخ عمليات

20200823103624.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y