Floquet modes and stability analysis of periodic orbit-attitude solutions along Earth–Moon halo orbits

Stability of halo orbits.

We predict new populations of trapped nonequatorial ("halo") orbits of charged dust grains about an arbitrary axisymmetric planet. Simple equilibrium and stability conditions are derived, revealing dramatic differences between positively and negatively charged grains in prograde or retrograde orbits. Implications for the Cassini mission to Saturn are discussed.

Stability Analysis of Periodic Orbits in Digital Spiking Neurons

Rigorous Numerics in Floquet Theory: Computing Stable and Unstable Bundles of Periodic Orbits

In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental matrix solution Φ(t) is a canonical decomposition of the form Φ(t) = Q(t)e, where Q(t) is a real periodic matrix and R is a constant matrix. To compute rigorously the Fl...

Computation and Stability of Periodic Orbits of Nonlinear Mappings

In this paper, we first present numerical methods that allow us to compute accurately periodic orbits in high dimensional mappings and demonstrate the effectiveness of our methods by computing orbits of various stability types. We then use a terminology for the different stability types, which is perfectly suited for systems with many degrees of freedom, since it clearly reflects the configurat...

STABILITY OF LARGE PERIODIC SOLUTIONS OF KLEIN-GORDON NEAR A HOMOCLINIC ORBIT by

— We consider the Klein-Gordon equation (KG) on a Riemannian surface M ∂ t u−∆u−mu+ u = 0, p ∈ N, (t, x) ∈ R×M, which is globally well-posed in the energy space. Viewed as a first order Hamiltonian system in the variables (u, v ≡ ∂tu), the associated flow lets invariant the two dimensional space of (u, v) independent of x. It turns out that in this invariant space, there is a homoclinic orbit t...