Recent Advances in Dynamical Astronomy Proceedings of the NATO Advan
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 Usi
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ASTROPHYSICS AND SPACE SCIENCE LIBRARY A SERIES OF BOOKS ON THE RECENT DEVELOPMENTS OF SPACE SCIENCE AND OF GENERAL GEOPHYSICS AND ASTROPHYSICS PUBLISHED IN CONNECTION WITH THE JOURNAL SPACE SCIENCE REVIEWS
Editorial Board J.
E. BLAMONT, Laboratoire d'Aeronomie, Verrieres, France R. L. F. BOYD, University College, London, England
L.
GOLDBERG,
Kilt Peak National Observatory, Tucson, Ariz., U.S.A.
C. DE JAGER,
University of Utrecht, Holland
Z. KOPAL, University of Manchester, Manchester, England
9. H. LUDWIG, NOAA, National Environmental Satellite Service,
Suitland, Md., U.S.A.
R. LUST, Institut fiir Extraterrestrische Physik, Garching-Miinchen, Germany B. M. MCCORMAC,
Lockheed Palo Alto Research Laboratory, Palo Alto, Cali/., U.S.A.
H. N. ~EWE~L, /VASA" WashipK,ton, D.C., U.S.A.
L. I.
SEDOV,
Acad~;;'~o/ Scie~ces ~hh~ 'riS.S.R., Moscow,
Z.
SVESTKA,
U.S.S.R.
Freiburg im Breisgau, Germany
Secretary of the Editorial Board
w. DE GRAAFF, Sterrewacht 'Sonnenborgh', University of Utrecht, Utrecht, Holland
VOLUME 39
RECENT ADVANCES IN DYNAMICAL ASTRONOMY PROCEEDINGS OF THE NATO ADVANCED STUDY INSTITUTE IN DYNAMICAL ASTRONOMY HELD IN CORTINA D'AMPEZZO, ITALY, AUGUST 9-21, 1972
Edited by
B. D. TAPLEY AND V. SZEBEHEL Y Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, Tex. 78712, U.S.A.
D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND
I BOSTON-U.S.A.
Library of Congress Catalog Card Number 73-83571
ISBN-13: 978-94-010-2613-0
e-ISBN-13: 978-94-010-261 1-6
DOl: 10. 1007/978-94-0 I 0-26 I 1-6
Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada and Mexico by D. Reidel Publishing Company, Inc. 306 Dartmouth Street, Boston, Mass. 02116, U.S.A.
All Rights Reserved Copyright © 1973 by D. Reidel Publishing Company, Dordrecht, Holland Soflcover reprint of the hardcover 1st edition 1973 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher
TABLE OF CONT'E'N"FS···
VII
PREFACE LIST OF PRINCIPAL SPEAKERS
IX
LIST OF PARTICIPANTS
XI
1. REGULARIZATION E. STIEFEL /
A Linear Theory of the Perturbed Two-Body Problem (Regular-
ization) Collision Singularities in Gravitational Problems Regularization Using a Time-Transformation Only J. BAUMGAR TE / Stabilization of the Differential Equations of Keplerian Motion F. NAHON / The Particular Solutions of Levi-Civita O. GODAR T / Example ofIntegration of Strongly Oscillating Systems w. BLACK / The Application of Recurrence Relations to Special Perturbation Methods D. G. BETTIS / Numerical Solution of Ordinary Differential Equations (Abstract) J. WALDVOGEL /
D. C. HEGGIE /
3 21 34 38 45 53 61 71
II. THE THREE-BODY PROBLEM V. SZEBEHELY /
Recent Advances in the Problem of Three Bodies Periodic Elliptic Motion in the Problem of Three Bodies
75
R. F. ARENSTORF /
(Abstract) and c. L. GOUDAS / On a Conjecture by Poincare G. KATSIARIS / The Three-Dime
