%0 Journal Article %1 springerlink:10.1007/s10910-012-0057-z %A Paşca, Daniel %A Valls, Cláudia %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K ODEs analysis classical mathematics mechanics physics qualitative %N 10 %P 2671-2688 %R 10.1007/s10910-012-0057-z %T Qualitative analysis of the anisotropic two-body problem with generalized Lennard-Jones potential %U http://dx.doi.org/10.1007/s10910-012-0057-z %V 50 %X This paper continue the study of the generalized Lennard-Jones potential started in Bărbosu et al. (J Math Chem 49(9):1961–1975, 2011 ) for a more general situation. More precisely we study the two-body problem with generalized Lennard-Jones potential in an anisotropic space. We will show that the set of initial conditions leading to collisions and ejections have positive measure. We also study the capture and escape solutions in the zero-energy case using the infinity manifold. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and the two anisotropic perturbations corresponding to the generalized Lennard-Jones potential is chaotic.

@article{springerlink:10.1007/s10910-012-0057-z, abstract = {This paper continue the study of the generalized Lennard-Jones potential started in Bărbosu et al. (J Math Chem 49(9):1961–1975, 2011 ) for a more general situation. More precisely we study the two-body problem with generalized Lennard-Jones potential in an anisotropic space. We will show that the set of initial conditions leading to collisions and ejections have positive measure. We also study the capture and escape solutions in the zero-energy case using the infinity manifold. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and the two anisotropic perturbations corresponding to the generalized Lennard-Jones potential is chaotic.}, added-at = {2012-10-27T13:55:08.000+0200}, affiliation = {Department of Mathematics and Informatics, University of Oradea, University Street 1, 410087 Oradea, Romania}, author = {Paşca, Daniel and Valls, Cláudia}, biburl = {https://www.bibsonomy.org/bibtex/220fee79a7fbdd56ce7fbfcab6c6dadc6/drmatusek}, doi = {10.1007/s10910-012-0057-z}, interhash = {ae6d2356aa9769ee045658281f88a4df}, intrahash = {20fee79a7fbdd56ce7fbfcab6c6dadc6}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {ODEs analysis classical mathematics mechanics physics qualitative}, month = nov, number = 10, pages = {2671-2688}, publisher = {Springer Netherlands}, timestamp = {2012-12-10T18:11:33.000+0100}, title = {Qualitative analysis of the anisotropic two-body problem with generalized Lennard-Jones potential}, url = {http://dx.doi.org/10.1007/s10910-012-0057-z}, volume = 50, year = 2012 }