Abstract:
In this work we have given a Hamiltonian formulation to Robe's problem, obtaining again the classic results. We have computed the resonances existing in the circular case and obtained some information with regard to the linear stability of the central equilibrium of Robe's problem in the elliptic case. In some critical cases we have constructed, in the parameter plane, the boundary curves that separate the regions of stability and instability.
\Bibitem{Val16}
\by Lucas Rezende Valeriano
\paper Parametric Stability in Robe's Problem
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 1
\pages 126--135
\mathnet{http://mi.mathnet.ru/rcd70}
\crossref{https://doi.org/10.1134/S156035471601007X}
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This publication is cited in the following 9 articles:
Adecarlos C. Carvalho, Gerson C. Araujo, “Parametric Resonance of a Charged Pendulum
with a Suspension Point Oscillating Between Two Vertical
Charged Lines”, Regul. Chaotic Dyn., 28:3 (2023), 321–331
Hildeberto E. Cabral, Lúcia Brandão Dias, Applied Mathematical Sciences, 218, Normal Forms and Stability of Hamiltonian Systems, 2023, 261
Yocelyn Péerez-Rothen, Lucas Rezende Valeriano, Claudio Vidal, “On the Parametric Stability of the Isosceles Triangular
Libration Points in the Planar Elliptical Charged Restricted
Three-body Problem”, Regul. Chaotic Dyn., 27:1 (2022), 98–121
José Laudelino de Menezes Neto, Gerson Cruz Araujo, Yocelyn Pérez Rothen, Claudio Vidal, “Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit”, JGM, 14:3 (2022), 381
A. A. Burov, V. I. Nikonov, “Libration Points Inside a Spherical Cavity of
a Uniformly Rotating Gravitating Ball”, Rus. J. Nonlin. Dyn., 17:4 (2021), 413–427
A. A. Burov, A. D. Guerman, V. I. Nikonov, “Equilibria in the gravitational field of a triangular body”, Celest. Mech. Dyn. Astron., 130:9 (2018), 58
A. A. Burov, A. D. German, I. I. Kosenko, V. I. Nikonov, “O prityazhenii ganteleobraznykh tel, predstavlennykh paroi peresekayuschikhsya sharov”, Nelineinaya dinam., 13:2 (2017), 243–256
D. Schmidt, L. Valeriano, “Nonlinear stability of stationary points in the problem of robe”, Discrete Contin. Dyn. Syst.-Ser. B, 21:6 (2016), 1917–1936
Dieter Schmidt, Lucas Valeriano, “Nonlinear stability of stationary points in the problem of Robe”, DCDS-B, 21:6 (2016), 1917
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