By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third authors, where the kinetic energy did not depend on the configuration coordinates.
@article{urn:eudml:doc:41695,
title = {Blow up of mechanical systems with a homogeneous energy.},
journal = {Publicacions Matem\`atiques},
volume = {35},
year = {1991},
pages = {335-345},
mrnumber = {MR1201560},
zbl = {0744.70019},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41695}
}
Lacomba, Ernesto A.; Bryant, John; Ibort, Luis Alberto. Blow up of mechanical systems with a homogeneous energy.. Publicacions Matemàtiques, Tome 35 (1991) pp. 335-345. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41695/