Navigation satellites are known from numerical studies to reside in a dynamically sensitive environment, which may be of profound importance for their long-term sustainability.We derive the fundamental Hamiltonian of Global Navigation Satellite System dynamics and show analytically that near-circular trajectories lie in the neighborhood of a Normally Hyperbolic Invariant Manifold (NHIM), which is the primary source of hyperbolicity. Quasicircular orbits escape through chaotic transport, regulated by NHIM’s stable and unstable manifolds, following a power law escape time distribution P(t) ∼ t^{−α}, with α ∼ 0.8 − 1.5. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics.
Chaotic transport of navigation satellites
DAQUIN, JEROME RAYMOND CHARLES;Efthymiopoulos C.
2019
Abstract
Navigation satellites are known from numerical studies to reside in a dynamically sensitive environment, which may be of profound importance for their long-term sustainability.We derive the fundamental Hamiltonian of Global Navigation Satellite System dynamics and show analytically that near-circular trajectories lie in the neighborhood of a Normally Hyperbolic Invariant Manifold (NHIM), which is the primary source of hyperbolicity. Quasicircular orbits escape through chaotic transport, regulated by NHIM’s stable and unstable manifolds, following a power law escape time distribution P(t) ∼ t^{−α}, with α ∼ 0.8 − 1.5. Our study is highly relevant for the design of satellite disposal trajectories, using manifold dynamics.
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