Montserrat Corbera has presented the oral communication “A special family of symmetric central configurations of the planar 3n-body problem” at the Conference “XIX Jornadas de Trabajo en Mecánica Celeste” held in Tudela from August 30 to September 1. The communication is a joint work with Claudia Valls from the Instituto Superior Técnico of the Universidade de Lisboa.
https://www.unavarra.es/mecanica-celeste
A special family of symmetric central configurations of the planar 3n–body problem
Abstract
We consider a particular type of symmetric central configurations of the planar 3n–body problem having n equal masses at the vertices of a regular n-gon inscribed on a circle of radius r and 2n masses at the vertices of either a regular or a semiregular concentric 2n–gon inscribed in a circle of radius ar. A semiregular 2n–gon is a 2n–gon having n pairs of vertices symmetric by a reflection of an angle β with respect to the axis of symmetry of the regular n–gon. For this type of symmetric central configurations it is known by symmetry that if the 2n–gon is regular then the masses at the 2n–gon alternate values, whereas if the 2n-gon is semiregular then all the masses at the 2n–gon must be equal. In this talk we analyze the set o values of a (when the 2n–gon is regular) and the set of values of (a, β) (when the 2n–gon is semiregular) that provide central configurations.
This is a joint work with Claudia Valls (Instituto Superior Técnico,Universidade de Lisboa).
∗montserrat.corbera@uvic.cat
Programa
LUNES 30 DE AGOSTO
- 8:30 – 9:00 – Recepción de los participantes y entrega de documentación en la entrada del Aulario del Campus de Tudela
- 9:00 – 9:30 – Apertura de las jornadas en el aula 202
- 9:30-11:00 – Sesión 1. Moderadora: Ana I. Pascual
09:30 – 10:00 – A. Elipe: “Orbital elements evolution in the two-body problem with slowly decreasing mass”
10:00 – 10:30 – E. Barrabés: “Colisiones de átomos de He sobre una superficie de Cu: soluciones oscilatorias”
10:30 – 11:00 – E. Fantino: “Design of a low-energy, low-thrust trajectory to Saturn and its inner moons“ - 11:00 – 11:30 – Pausa para el café
- 11:30 – 13:30 – Sesión 2. Moderador: Manuel Iñarrea
11:30 – 12:00 – F.A. Soler: “Equilibrios relativos de un modelo 2-DOF Hr, ν para el movimiento roto-orbital”
12:00 – 12:30 – J.J. Costa: “Coefficients of the gravitational potential of a rigid body and inertia integrals”
12:30 – 13:00 – E.A. Turner: “Reduction and relative equilibria in the full gravitational N-body problem”
13:00 – 13:30 – L. Rández: “On the integral solution of elliptic Kepler equation: on the practical implementation“ - 13:30 – 15:30 – Comida en el restaurante Topero
- 15:30 – 17:00 – Sesión 3. Moderadora: Montserrat Corbera
15:30 – 16:00 – J.L. Cornelio: “Central configurations in the five-body problem: Rhombus plus one”
16:00 – 16:30 – D. Mortari: “The theory of functional connections: current status”
16:30 – 17:00 – D. Casanova: “Searching space debris associations“ - 17:00 – Foto de grupo
- 18:00 – Salida en autobús desde el Sercotel Tudela Bardenas para ir a hacer una visita guiada a las Bardenas Reales
- 20:00 – Llegada al centro de interpretación de Aguilares en las Bardenas donde disfrutaremos de un piscolabis
- 21:00 – Charla-observación astronómica pública: “De paseo por el cielo de las Bardenas”, por José Ángel Docobo
- 22:00 – Traslado en autobús al Sercotel Tudela Bardenas
MARTES 31 DE AGOSTO
- 9:00 – 11:00 – Sesión 4. Moderador: Teo Roldán
09:00 – 09:30 – J.P. Salas: “Chaos and thermalization in dynamical systems with many degrees of freedom”
09:30 – 10:00 – P. Sánchez: “A dynamical analysis of four-armed barred galaxies”
10:00 – 10:30 – E. Tresaco: “Invariant manifolds for the dipole-segment problem”
10:30 – 11:00 – B. Nicolás: “Transport phenomena and capture of an asteroid near L3 in a Sun-perturbed Earth-Moon system“ - 11:00 – 11:30 – Pausa para el café
- 11:30 – 13:30 – Sesión 5. Moderador: Josep M. Cors
11:30 – 12:00 – G. Duarte: “Fast Arnold diffusion in the Sun-Jupiter system”
12:00 – 12:30 – O. Rodríguez: “Ejection-collision orbits in the RTBP from a numerical to an analytical point of view”
12:30 – 13:00 – M. Giralt: “Breakdown of homoclinic orbits to L3 in the RPC3BP”
13:00 – 13:30 – D. Arnas: “On the application of operator theory to the zonal harmonics problem about an oblate celestial body“ - 13:30 – 15:30 – Comida en el restaurante Topero
- 15:30 – 18:00 – Sesión 6. Moderador: Antonio Elipe
15:30 – 16:00 – J.A. Zepeda: “Nonlinear stability of equilibrium points in the planar equilateral restricted mass-unequal four-body problem”
16:00 – 18:00 – Homenaje a José Ángel Docobo por su 70 cumpleaños y a los profesores que se han ido jubilando a lo largo de los años en los que hemos celebrado las jornadas - 18:30-19:30 – Visita guiada a la ciudad de Tudela
- 20:00 – Salida en autobús desde el Sercotel Tudela Bardenas para ir a cenar al restaurante Pago de Cirsus
MIÉRCOLES 1 DE SEPTIEMBRE
- 9:00 – 11:00 – Sesión 7. Moderador: Pedro Pablo Campo
09:00 – 09:30 – J.J. Morales: “A differential Galois approach to path integrals”
09:30 – 10:00 – L. Floría: “The gravitational parameter as a canonical element in hyperbolic–type motion”
10:00 – 10:30 – M. Corbera: “A special family of symmetric central configurations of the planar 3n–body problem”
10:30 – 11:00 – J.M. Cors: “On (κ,n)-crowns“ - 11:00 – 11:30 – Pausa para el café
- 11:30 – 13:30 – Sesión 8. Moderador: Víctor Lanchares
11:30 – 12:00 – J.A. López: “Análisis de una nueva anomalía simétrica en el problema de dos cuerpos”
12:00 – 12:30 – A. Pousse: “On the averaged problem in the case of mean-motion resonances and the computation of solutions in the restricted three-body problem. Rigorous treatment and application to co-orbital motions”
12:30 – 13:00 – C. Vázquez: “Long-term perturbations in four-body systems with mutual highly inclined orbits”
13:00 – 13:30 – C. Abad: “Relaxmetría“ - 13:30 – 15:30 – Comida en el restaurante Topero/
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