%0 Journal Article %1 springerlink:10.1007/s10910-011-9867-7 %A Bărbosu, Mihail %A Mioc, Vasile %A Paşca, Daniel %A Szenkovits, Ferenc %D 2011 %I Springer Netherlands %J Journal of Mathematical Chemistry %K ODEs analysis classical mathematics mechanics physics qualitative %N 9 %P 1961-1975 %R 10.1007/s10910-011-9867-7 %T The two-body problem with generalized Lennard-Jones potential %U http://dx.doi.org/10.1007/s10910-011-9867-7 %V 49 %X We consider a generalization of the famous Lennard-Jones potential. To study the two-body problem associated to this potential, we use the foliations of the phase space by the invariant sets corresponding to the first integrals of energy and angular momentum. We investigate all possible situations created by the interplay among the constants of integration and the field parameters. We obtain the global flow, and illustrate it in both 3D and 2D. This flow exhibits a great variety of orbits, a homoclinic one included. All phase portraits are interpreted in terms of physical trajectories.

@article{springerlink:10.1007/s10910-011-9867-7, abstract = {We consider a generalization of the famous Lennard-Jones potential. To study the two-body problem associated to this potential, we use the foliations of the phase space by the invariant sets corresponding to the first integrals of energy and angular momentum. We investigate all possible situations created by the interplay among the constants of integration and the field parameters. We obtain the global flow, and illustrate it in both 3D and 2D. This flow exhibits a great variety of orbits, a homoclinic one included. All phase portraits are interpreted in terms of physical trajectories.}, added-at = {2011-09-23T03:22:45.000+0200}, affiliation = {Department of Mathematics, The College at Brockport, State University of New York, 350 New Campus Dr. Brockport, Brockport, NY 14420, USA}, author = {Bărbosu, Mihail and Mioc, Vasile and Paşca, Daniel and Szenkovits, Ferenc}, biburl = {https://www.bibsonomy.org/bibtex/23ac2f74200936e6b7893164cf382bdf7/drmatusek}, description = {SpringerLink - Journal of Mathematical Chemistry, Volume 49, Number 9}, doi = {10.1007/s10910-011-9867-7}, interhash = {43768e0ef9a0b69da3b66c2a3371c14b}, intrahash = {3ac2f74200936e6b7893164cf382bdf7}, issn = {0259-9791}, issue = {9}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {ODEs analysis classical mathematics mechanics physics qualitative}, month = {October}, number = 9, pages = {1961-1975}, publisher = {Springer Netherlands}, timestamp = {2012-11-12T00:55:42.000+0100}, title = {The two-body problem with generalized Lennard-Jones potential}, url = {http://dx.doi.org/10.1007/s10910-011-9867-7}, volume = 49, year = 2011 }