Hamiltonian Systems and Celestial Mechanics (HAMSYS-98) : proceedings of the III International Symposium : Patzcuaro, Michoaan, Mexico, 7-11 December 1998 / editors J. Delgado ... [et al.].

Format:

Book

Conference/Event

Contributor:

Delgado, J. (Joaquín)

Conference Name:

International Symposium on Hamiltonian Systems and Celestial Mechanics (3rd : 1998 : Patzcuaro, Mexico)

Series:

World scientific monograph series in mathematics ; v. 6.

World scientific monograph series in mathematics ; vol. 6

Language:

English

Subjects (All):

Hamiltonian systems--Congresses.

Hamiltonian systems.

Celestial mechanics--Congresses.

Celestial mechanics.

Physical Description:

1 online resource (373 p.)

Other Title:

HAMSYS-98

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2000.

Language Note:

English

Summary:

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.

Contents:

PREFACE; CONTENTS; THE RHOMBOIDAL CHARGED FOUR BODY PROBLEM; 1 Introduction; 2 Equations of motion; 3 McGehee coordinates; 4 The potential function U(θ); 5 Global flow on the total collision manifold; 5.1 Global flow on Λ1, Λ3, Λ5, Λ7; 6 Global flow for h = 0; References; PLANETARY RINGS WITH SHEPHERDS; References; LOW REYNOLDS NUMBER SWIMMING IN TWO DIMENSIONS; 1 Introduction; 2 The planar swimmer; 2.1 Stokes Equations in the plane; 2.2 Shapere-Wilczek's Connection and Curvature Forms; 3 The Elliptical Swimmer (following the SW recipe); 3.1 Examples and discussion

4 Mathematical details and corrections to SW4.1 The canonical vs. the hodographed Fourier basis; 4.2 Total force and total torque; 4.3 The 1-form of the connection; 4.4 Infinitesimal rotations: corrected formula; 4.5 The ellipse. Rotational components; 5 Power expenditure; 5.1 The differential form fds = gdθ; 5.2 Computing g for the ellipse; negative Fourier modes; 5.3 Hypotrochoids; 6 Efficiency of an elliptic microswimmer; 6.1 The variational problem; 6.2 Numerical results; Acknowledgments; Appendix; A. The Lie bracket; B. Curvatures for the ellipse using the canonical basis

C. Ellipse using the Fourier basis. More detailsD. Formula for the Force f; E. Matrices K and F for the elliptic swimmer; References; 2-DIMENSIONAL INVARIANT TORI FOR THE SPATIAL ISOSCELES 3-BODY PROBLEM; 1 Introduction; 2 Equations of motion of the isosceles problem; 3 Equations of motion of the reduced isosceles problem; 4 Relationships between the reduced isosceles problem and the isosceles problem; 5 Symmetric periodic orbits of the reduced isosceles problem; 6 Restricted isosceles problems; 6.1 The reduced circular Sitnikov problem; 6.2 Reduced elliptic Sitnikov problem

7 Continuation of periodic orbits8 2-dimensional invariant tori for isosceles problem; Acknowledgments; References; THE GLOBAL FLOW FOR THE SYNODICAL SPATIAL KEPLER PROBLEM; 1 Introduction; 2 Topological study of Hamiltonian systems; 3 Synodical spatial Kepler problem; 4 Topology of Ic, Ice and Icem; 5 Foliation of the phase space; References; UNBOUNDED GROWTH OF ENERGY IN PERIODIC PERTURBATIONS OF GEODESIC FLOWS OF THE TORUS; 1 Introduction; Riemannian Geometry; Scaled variables; The theory of normally hyperbolic manifolds; Averaging theory; KAM theory; Poincaré-Melnikov theory

Shadowing lemma2 The main steps of the proof; 2.1 Riemannian geometry and dynamics of the geodesic flow; 2.2 The scaled problem; 2.3 The inner and outer maps; 2.4 The perturbed invariant manifold. Normal hyperbolicity; 2.5 The perturbed inner map. Averaging theory; 2.6 The perturbed outer map. Poincaré-Melnikov theory; 2.7 Transition chains and shadowing orbits; 3 Some final remarks; Acknowledgements; References; SPLITTING AND MELNIKOV POTENTIALS IN HAMILTONIAN SYSTEMS; 1 Introduction; Setup; Main achievements; Motivation; Regular and singular cases; 2 The unperturbed Hamiltonian; Assumptions

The unperturbed torus and its homoclinic whisker

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9789812792099

9812792090