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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Minimizing Configurations and Hamilton–Jacobi Equations of Homogeneous $N$-body Problems
Ezequiel Maderna Centro de Matematica, Universidad de la Republica, Montevideo, Uruguay
Аннотация:
For $N$-body problems with homogeneous potentials we define a special class of central configurations related with the reduction of homotheties in the study of homogeneous weak KAM solutions. For potentials in $1/r^\alpha$ with $\alpha\in (0,2)$ we prove the existence of homogeneous weak KAM solutions. We show that such solutions are related to viscosity solutions of another Hamilton–Jacobi equation in the sphere of normal configurations. As an application we prove for the Newtonian three-body problem that there are no smooth homogeneous solutions to the critical Hamilton–Jacobi equation.
Ключевые слова:
$N$-body problem, central configuration, Hamilton–Jacobi.
Поступила в редакцию: 30.07.2013 Принята в печать: 23.10.2013
Образец цитирования:
Ezequiel Maderna, “Minimizing Configurations and Hamilton–Jacobi Equations of Homogeneous $N$-body Problems”, Regul. Chaotic Dyn., 18:6 (2013), 656–673
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd154 https://www.mathnet.ru/rus/rcd/v18/i6/p656
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