A characterization of the Ligon-Schaaf regularization map
First, we give an explicit description of all the mappings from the phace space of the Kepler problem to the phase space of the geodesics on the sphere, which transform the constants of motion of the Kepler problem to the angular momentum. Second, among these we describe those mappings which in addi...
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ftunivutrecht:oai:dspace.library.uu.nl:1874/2447 2023-07-23T04:20:53+02:00 A characterization of the Ligon-Schaaf regularization map Cushman, R.H. Duistermaat, J.J. 1996-01-01 application/pdf https://dspace.library.uu.nl/handle/1874/2447 en eng 0010-3640 https://dspace.library.uu.nl/handle/1874/2447 info:eu-repo/semantics/OpenAccess Wiskunde en Informatica Article 1996 ftunivutrecht 2023-07-01T22:44:30Z First, we give an explicit description of all the mappings from the phace space of the Kepler problem to the phase space of the geodesics on the sphere, which transform the constants of motion of the Kepler problem to the angular momentum. Second, among these we describe those mappings which in addition send Kepler solutions to parametrized geodesics. Third, we describe those mappings which in addition are canonical transformations of the respective phase space. Finally we prove that among these the Ligon-Schaaf map is the unique one which maps the collison orbits to the geodesics which pass through the north pole. In this way we also give a new proof that the Ligon-Schaaf map has all the properties described above. Article in Journal/Newspaper North Pole Utrecht University Repository North Pole |
institution |
Open Polar |
collection |
Utrecht University Repository |
op_collection_id |
ftunivutrecht |
language |
English |
topic |
Wiskunde en Informatica |
spellingShingle |
Wiskunde en Informatica Cushman, R.H. Duistermaat, J.J. A characterization of the Ligon-Schaaf regularization map |
topic_facet |
Wiskunde en Informatica |
description |
First, we give an explicit description of all the mappings from the phace space of the Kepler problem to the phase space of the geodesics on the sphere, which transform the constants of motion of the Kepler problem to the angular momentum. Second, among these we describe those mappings which in addition send Kepler solutions to parametrized geodesics. Third, we describe those mappings which in addition are canonical transformations of the respective phase space. Finally we prove that among these the Ligon-Schaaf map is the unique one which maps the collison orbits to the geodesics which pass through the north pole. In this way we also give a new proof that the Ligon-Schaaf map has all the properties described above. |
format |
Article in Journal/Newspaper |
author |
Cushman, R.H. Duistermaat, J.J. |
author_facet |
Cushman, R.H. Duistermaat, J.J. |
author_sort |
Cushman, R.H. |
title |
A characterization of the Ligon-Schaaf regularization map |
title_short |
A characterization of the Ligon-Schaaf regularization map |
title_full |
A characterization of the Ligon-Schaaf regularization map |
title_fullStr |
A characterization of the Ligon-Schaaf regularization map |
title_full_unstemmed |
A characterization of the Ligon-Schaaf regularization map |
title_sort |
characterization of the ligon-schaaf regularization map |
publishDate |
1996 |
url |
https://dspace.library.uu.nl/handle/1874/2447 |
geographic |
North Pole |
geographic_facet |
North Pole |
genre |
North Pole |
genre_facet |
North Pole |
op_relation |
0010-3640 https://dspace.library.uu.nl/handle/1874/2447 |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1772185710266155008 |