{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T21:35:19Z","timestamp":1719610519059},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,6]]},"abstract":" In the planar photogravitational Hill problem (PHP) three equivalent forms of the equations of motion are presented: the physical equations of motion and two more forms of the regularized equations of the problem. Using the Levi\u2013Civita coordinate transformation as well as the corresponding time transformation, we first obtain a simple regularized polynomial Hamiltonian of the dynamical system, and second the regularized equations of motion without using a regularized Hamiltonian. The relation between the physical and the regularized variables are also given. Zero velocity curves and surfaces, Poincar\u00e9 sections, families of symmetric periodic orbits as well as their stability are given in physical and regularized variables when the larger primary body (the sun) does not radiate and when it does. It is found that for large deviations of its value from the gravitational case, the radiation factor can have a strong effect on the structure of the families. Finally we present the stability regions in both cases with and without radiation using the maximal Lyapunov exponent (LE), working in the regularized equations of motion of the problem since through these the calculation of the stability is more rapid and accurate than using the physical equations of motion. <\/jats:p>","DOI":"10.1142\/s0218127406015696","type":"journal-article","created":{"date-parts":[[2006,8,31]],"date-time":"2006-08-31T07:05:57Z","timestamp":1157007957000},"page":"1809-1821","source":"Crossref","is-referenced-by-count":9,"title":["THE PLANAR PHOTOGRAVITATIONAL HILL PROBLEM"],"prefix":"10.1142","volume":"16","author":[{"given":"K. E.","family":"PAPADAKIS","sequence":"first","affiliation":[{"name":"Department of Engineering Sciences, Division of Applied Mathematics and Mechanics, University of Patras, GR-26504 Patras, Greece"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.18.1183"},{"key":"rf2","first-page":"992","volume":"28","author":"H\u00e9non H.","journal-title":"Ann. Astrophys."},{"key":"rf3","first-page":"223","volume":"1","author":"H\u00e9non H.","journal-title":"Ann. Astrophys."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02419867"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2184-3"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026238123759"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00640021"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1002487228086"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008209210002"},{"key":"rf10","volume-title":"Recent Advances in Mechanics and Related Fields","author":"Papadakis K. E.","year":"2004"},{"key":"rf11","first-page":"250","volume":"27","author":"Radzievskii V. V.","journal-title":"Astron. Zh"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00645009"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1086\/157989"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01227667"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00211-0"},{"key":"rf16","volume-title":"Theory of Orbits","author":"Szebehely V. G.","year":"1967"},{"key":"rf17","volume-title":"The Dynamics of Small Bodies in the Solar System","author":"Waldvogel J.","year":"1999"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406015696","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:10:06Z","timestamp":1565122206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406015696"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":17,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1142\/S0218127406015696"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406015696","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}