A dissipative Kepler problem with a family of singular drags
Sign Up to like & getrecommendations! Published in 2020 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-020-9956-7
Abstract: In this work, we consider the Kepler problem with a family of singular dissipations of the form $$-\frac{k}{|x|^\beta }\dot{x},\quad k>0, \beta >0.$$ - k | x | β x ˙ , k > 0 ,… read more here.
Keywords: problem family; kepler problem; family singular;
McGehee Blow-Up of the Kepler Problem on Surfaces of Constant Curvature
Sign Up to like & getrecommendations! Published in 2020 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-020-00349-6
Abstract: In this work we address the local behaviour at collision of the Kepler problem on surfaces of constant curvature. A full description of dynamics in the extended energy surface is given relying in the energy… read more here.
Keywords: problem surfaces; kepler problem; surfaces constant; constant curvature ... See more keywords
Kepler problem and chiral effective dynamics.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.106.064207
Abstract: It is shown that by an appropriate canonical transformation, Kepler dynamics can be put in the form which allows one to exhibit the structure of the symmetry transformations related to the superintegrability. They appear to… read more here.
Keywords: problem chiral; kepler problem; chiral effective; kepler ... See more keywords
Adaptive symplectic conservative numerical methods for the Kepler problem
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DOI: 10.1134/s0012266117070096
Abstract: We suggest and substantiate a unified form of a family of adaptive conservative numerical methods for the Kepler problem. The family contains methods of the second, fourth, and sixth approximation order as well as an… read more here.
Keywords: methods kepler; kepler problem; conservative numerical; numerical methods ... See more keywords
Planetary Systems and the Hidden Symmetries of the Kepler Problem
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DOI: 10.3390/sym12122109
Abstract: The question of whether the solar distances of the planetary system follow a regular sequence was raised by Kepler more than 400 years ago. He could not prove his expectation, inasmuch as the planetary orbits… read more here.
Keywords: systems hidden; kepler problem; planetary systems; symmetries kepler ... See more keywords
Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problem on the Sphere
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DOI: 10.4153/cjm-2016-050-1
Abstract: Abstract We study a second-order ordinary differential equation coming from the Kepler problem on ${{\mathbb{S}}^{2}}$ . The forcing term under consideration is a piecewise constant with singular nonlinearity that changes sign. We establish necessary and… read more here.
Keywords: solutions indefinite; equation; kepler problem; periodic solutions ... See more keywords