Recent Advances in Dynamical Astronomy

1. Front Matter

   Pages I-XIII

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2. Regularization

   1. Front Matter

      Pages 1-1

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   2. A Linear Theory of the Perturbed Two-Body Problem (Regularization)

      • E. Stiefel

      Pages 3-20

   3. Collision Singularities in Gravitational Problems

      • J. Waldvogel

      Pages 21-33

   4. Regularization Using a Time-Transformation Only

      • D. C. Heggie

      Pages 34-37

   5. Stabilization of the Differential Equations of Keplerian Motion

      • J. Baumgarte

      Pages 38-44

   6. The Particular Solutions of Levi-Civita

      • F. Nahon

      Pages 45-52

   7. Example of Integration of Strongly Oscillating Systems

      • O. Godart

      Pages 53-60

   8. The Application of Recurrence Relations to Special Perturbation Methods

      • W. Black

      Pages 61-70

   9. Numerical Solution of Ordinary Differential Equations

      • D. G. Bettis

      Pages 71-71

3. The Three-Body Problem

   1. Front Matter

      Pages 73-73

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   2. Recent Advances in the Problem of Three Bodies

      • V. Szebehely

      Pages 75-106

   3. Periodic Elliptic Motion in the Problem of Trhee Bodies

      • R. F. Arenstorf

      Pages 107-108

   4. On a Conjecture by Poincaré

      • G. Katsiaris, C. L. Goudas

      Pages 109-117

   5. The Three-Dimensional Elliptic Problem

      • G. Katsiaris

      Pages 118-134

   6. Second and Third Order Variations of the Three Dimensional Restricted Problem

      • P. G. Kazantzis

      Pages 135-145

   7. Planar Periodic Orbits Using Second and Third Variations

      • C. G. Zagouras

      Pages 146-155

   8. Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points

      • E. Rabe

      Pages 156-160

   9. A Linear Description of the Second Species Solutions

      • P. Guillaume

      Pages 161-174

4. The N-Body Problem and Stellar Dynamics

   1. Front Matter

      Pages 175-175

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IX LIST OF PRINCIPAL SPEAKERS XI LIST OF PARTICIPANTS 1. REGULARIZATION E. STIEFEL / A Linear Theory of the Perturbed Two-Body Problem (Regul- ization) 3 J. WALDVOGEL / Collision Singularities in Gravitational Problems 21 D. C. HEGGIE / Regularization Using a Time-Transformation Only 34 J. BAUMGAR TE / Stabilization of the Differential Equations of Keplerian Motion 38 F. NAHON / The Particular Solutions of Levi-Civita 45 O. GODAR T / Example ofIntegration of Strongly Oscillating Systems 53 w. BLACK / The Application of Recurrence Relations to Special Perturbation Methods 61 D. G. BETTIS / Numerical Solution of Ordinary Differential Equations (Abstract) 71 II. THE THREE-BODY PROBLEM V. SZEBEHELY / Recent Advances in the Problem of Three Bodies 75 R. F. ARENSTORF / Periodic Elliptic Motion in the Problem of Three Bodies (Abstract) 107 G. KATSIARIS and c. L. GOUDAS / On a Conjecture by Poincare 109 G. KATSIARIS / The Three-Dimensional Elliptic Problem 118 P. G. KAZANTZIS / Second and Third Order Variations of the Three Dimensional Restricted Problem 135 c. G. ZAGOURAS / Planar Periodic Orbits Using Second and Third Variations 146 E. RABE / Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points 156 P. GUILLAUME / A Linear Description of the Second Species Solutions 161 III. THE N-BODY PROBLEM AND STELLAR DYNAMICS G. CONTOPOULOS / Problems of Stellar Dynamics 177 w. T. KYNER / Invariant Manifolds in Celestial Mechanics 192 s. J.

• Celestial mechanics
• Variation
• astronomy
• gravitation
• gravity
• planet
• solar system
• star
• sun
• turbulence
• two-body problem

• Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, USA

  B. D. Tapley, V. Szebehely

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