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  • Produktbild: Linear and Regular Celestial Mechanics
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Band 174

Linear and Regular Celestial Mechanics Perturbed Two-body Motion Numerical Methods Canonical Theory

Aus der Reihe Grundlehren der mathematischen Wissenschaften

107,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2011

Verlag

Springer Berlin

Seitenzahl

306

Maße (L/B/H)

23,5/15,5/1,8 cm

Gewicht

492 g

Auflage

1971

Sprache

Englisch

ISBN

978-3-642-65029-1

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2011

Verlag

Springer Berlin

Seitenzahl

306

Maße (L/B/H)

23,5/15,5/1,8 cm

Gewicht

492 g

Auflage

1971

Sprache

Englisch

ISBN

978-3-642-65029-1

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

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  • Produktbild: Linear and Regular Celestial Mechanics
  • Produktbild: Linear and Regular Celestial Mechanics
  • I Basic and Numerical Theory.- I Preliminaries.- 1. Laws of Motion.- Motion about a Central Mass.- Perturbed Motion.- 2. Energy Relations.- Perturbing Potential.- 3. Collection of Formulae.- 4. Singular Differential Equations.- 5. One-Dimensional Motion.- First Step of Regularization.- Second Step of Regularization.- The Harmonic Oscillator.- II Regularized Theory.- 6. Matrices.- 7. Fictitious lime.- 8. Motion in a Plane.- 9. Motion in Space.- The KS-Matrix.- Equations of Motion.- Energy Relations.- Regularized Equations.- Comments.- Further Aids.- Collection of Formulae.- III Kepler Motion.- 10. Elliptic Motion.- Geometric Properties.- Dynamics of Elliptical Motion.- 11. Uniform Treatment of the Three Varieties of Pure Kepler Motion.- Stumpff Functions.- Kepler Motion in Terms of the c-Functions.- Collection of Formulae.- IV The Initial Value Problem.- 12. Shape and Position of the Orbit.- 13. Use of the KS-Transformation.- Pure Motion in Parametric Representation.- The Parametric Initial Value Problem.- The Osculating Orbit.- Collection of Formulae.- The Problem of the Projectile.- Critical Initial Data.- 14. The Classical Elements.- Collection of Formulae.- 15. Numerical Examples.- V The Fundamental Differential Equations.- 16. Stability.- Comments.- 17. Numerical Aspects.- Regulation of the Step Size.- Error Propagation.- 18. The Time-Element.- The General Concept of Elements.- of a Time-Element.- Collection of Formulae.- Comments.- 19. A Set of Regular Elements.- Collection of Formulae.- Comments.- The u-Method.- Appendix. Orthogonal Elements.- VI Typical Perturbations.- 20. Gravitational Potentials.- Clusters and Rigid Bodies.- Speroids.- Example.- 21. Oblateness Perturbations.- The r-Equation.- Comments.- 22. Third Body Attraction.- The Interior Problem.- Rule for Adjustment of the Perturbing Potential (Interior Problem).- The Exterior Problem.- Comments.- 23. Numerical Examples.- Adaptation of the Element Equations (19,61)-(19,63) to Automatic Computation.- General Description of the Experiments.- Examples 1–6.- VII Refmed Numerical Methods.- 24. Difference Methods.- Derivation of the Modified Coefficients.- Collection of Formulae.- 25. Applications to Differential Equations.- Application to Celestial Mechanics.- Long Term Numerical Behaviour.- 26. Refinement of Taylor Expansions.- Definitions and Properties of a Sequence of Functions.- On Solving Differential Equations by Power Expansions.- Finite Power- and G-Expansions.- Algorithm.- Remarks.- 27. Application to Satellite Motion.- Oblateness Perturbation.- Comments.- Third Body Attraction.- Final Remark Concerning Sections 24 to 27.- 28. First Order Methods.- Third Body Perturbation.- Comments.- Convergence of Fourier Expansions.- Expansion with Respect to a Perturbing Parameter.- II Canonical Theory.- VIII General Canonical Theory.- 29. Preliminaries.- Dynamics of n Point Masses.- General Canonical Systems.- 30. Homogeneous Formalism.- Law of Energy.- Homogeneous Systems.- 31. Canonical Transformations.- 32. Generating Function.- Independent Variable Appearing Explicitly in a Transformation.- 33. Construction of Canonical Transformations.- Transformation of the Coordinates.- Jacobi’s Method of Integration.- Elements and their Perturbations.- 34. New Independent Variable, Scaling Factors.- IX Classical Canonical Theory of the Perturbations of Elements.- 35. Delaunay Elements.- Spherical Coordinates.- Jacobi’s Integration Method.- Canonical and Classical Elements.- Delaunay Elements.- 36. Perturbation of Elements.- Perturbation of the Delaunay Elements.- Perturbation of the Classical Elements.- Secular Differential Equations.- X The Canonical Theory of the Oscillator Generated by the Perturbed Problem of two Bodies.- 37. Introduction of new Independent Variables.- 38. The Canonical KS-Transformation.- Motion in Space, Canonical KS-Transformation.- Fundamental Theorem.- The Basic Canonical System with Respect to the Fictitious Time s.- The Basic Canonical System with Respect to the Generalized Eccentric Anomaly E.- 39. Canonical Forces.- The System in the Fictitious Time s.- The System in the Generalized Eccentric Anomaly E.- 40. Canonical Oscillator Elements in the Fictitious Time Version.- Separation of Jacobi’s Equation.- Uniform Treatment of the Element Equations.- Uniformly Regular Canonical Elements.- The Basic Element System with Respect to the Fictitious Time s.- 41. Canonical Oscillator Elements in the Generalized Eccentric Anomaly Version.- The Basic System with Respect to the Generalized Eccentric Anomaly E.- Canonical Forces.- 42. First Views on Analytical Perturbation Methods.- Literal Expression of the Perturbing Potential as a Function of the Canonical Oscillator Elements.- Analytical First Order Perturbations.- Comments Concerning Chapters IX and X.- III Geometry and Outlook.- XI Geometry of the KS-Transformation.- 43. The Fourdimensional Space.- The Fibration of U4.- The Mapping of Curves.- Planes of Levi-Civita’s Type.- Remarks.- The Cayley Matrix.- A Cross Product.- Remarks.- 44. The Mapping of the Spheres.- The Fibration of S3.- The Inverse Mapping of Curves.- Quaternions.- Topological Aids.- 45. The Manifold of Kepler Orbits.- Outlook.- References.- Author and Subject Index.