Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori

Iñarrea, Manuel; Lanchares, Víctor; Palacián, Jesús F.; Pascual, Ana I.; Salas, J. Pablo; Yanguas, Patricia

doi:10.1016/j.physd.2012.02.017

Cited by 4 publications

(16 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, if β = (−7δ 2 + 6 J 2 L 2 + 6δL 3 )/(2δL 6 ), the quadratic part ofH is in resonance 1:1. This is the precise value of β where most of the bifurcation lines of the two-reduced space are confluent, see [24], although no bifurcation occurs on S 2 × S 2 . If β = (4δ 2 + 3 J 2 L 2 )/(4δL 6 ) the system is in resonance 1:−2.…”

Section: Circular Equatorial Solutionsmentioning

confidence: 95%

“…This analysis has to be performed on S 2 × S 2 , combining the global coordinates a and b with the local coordinates given by x i 's and y i 's in Section 3. In [24], using the Hamiltonian function of (21) we have extended the previous research of [21,22], as we take into account the oblateness coefficient of the planet. Moreover, the reconstruction of the flow of the original system from the flow in the twice-reduced space is rigorously done, concluding the existence of some invariant tori together with different types of bifurcations of them.…”

Section: Hamiltonian Modelmentioning

confidence: 99%

“…Moreover, the reconstruction of the flow of the original system from the flow in the twice-reduced space is rigorously done, concluding the existence of some invariant tori together with different types of bifurcations of them. Furthermore, the existence of some KAM tori is also established in [24]. However, not all the information about the dynamics of Hamiltonian (21) can be recovered from the flow in the twice-reduced phase space.…”

Section: Hamiltonian Modelmentioning

confidence: 99%

“…Furthermore, there are other features of the system that need to be analysed in the first-reduced phase space, that is, on S 2 × S 2 . Hence, the study we perform along the paper must be understood complementary to that of [24].…”

Section: Hamiltonian Modelmentioning

confidence: 99%

“…Indeed, this plane of bifurcations contains two special points related to circular equatorial motions where all the bifurcation curves are coincident-see [24], and also [21]-where we analysed a simplified version of the generalised Størmer problem and only one of the two points was present in the study. However, these points are limit situations of the behaviour of the flow corresponding with the twice-reduced space as this space gets reduced to points for circular equatorial trajectories.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Symplectic coordinates onS2×S2for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

Iñarrea

Lanchares

Palacián

et al. 2011

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

In order to analyse the dynamics of a given Hamiltonian system in the space defined as the Cartesian product of two spheres, we propose to combine Delaunay coordinates with Poincaré-like coordinates. The coordinates are of local character and have to be selected accordingly with the type of motions one has to take into consideration, so we distinguish the following types: (i) rectilinear motions; (ii) circular and equatorial motions; (iii) circular nonequatorial motions; (iv) non-circular equatorial motions; and (v) non-circular and non-equatorial motions. We apply the theory to study the dynamics of the reduced flow of a generalised Størmer problem that is modelled as a perturbation of the Kepler problem. After using averaging and reduction theories, the corresponding flow is analysed on the manifold S 2 × S 2 , calculating the occurring equilibria and their stability. Finally, the flow of the original problem is reconstructed, concluding the existence of some families of periodic solutions and KAM tori.

show abstract

Section: Circular Equatorial Solutionsmentioning

confidence: 95%

Section: Hamiltonian Modelmentioning

confidence: 99%

Section: Hamiltonian Modelmentioning

confidence: 99%

Section: Hamiltonian Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Symplectic coordinates onS2×S2for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

Iñarrea

Lanchares

Palacián

et al. 2011

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

show abstract

Effects of a quadrupolar magnetic term in a generalized Störmer problem on dust grains

2023

View full text Add to dashboard Cite

Generalized Störmer and dynamical behavior of charged particles near magnetic planet

Leghmouche

Mebarki

2019

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

We study the motion of charged dust grains at arbitrary distants from a rotating magnetic planet,we show that the model treated for dipole field is an excellent approximation in most cases for a generalized Stormer problem, But that fundamentally new physics arises with the inclusion of a quadrupolar magnetic term. In particular,the appearence of a new trajectories for different kind of charged dust grains,which are meaningful when the individual and a comparable impact of the co-rotational and gravitational fields is considered.Furthermore,a detailed mathematical treatment of equilibrium state for various phase spaces for charged components in prograde or retrograde rotation direction with analytical solutions for a non linear parametric system.

show abstract

Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori

Cited by 4 publications

References 27 publications

Symplectic coordinates onS2×S2for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

Symplectic coordinates onS2×S2for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

Effects of a quadrupolar magnetic term in a generalized Störmer problem on dust grains

Generalized Störmer and dynamical behavior of charged particles near magnetic planet

Contact Info

Product

Resources

About