Optimal on-off cooperative manoeuvers for long-term satellite cluster flight

When a group of satellites is equipped with a particulary simple propul- sion system, e.g. cold-gas thrusters, constraints on the thrust level and total propellant mass renders cluster-keeping extremely challenging. This is even more pronounced in disaggregated space architectures, in which a satellite is formed by clustering a number of heterogenous, free-flying modules. The research described in this paper develops guidance laws aimed at keeping the relative distances between the cluster modules bounded for long mission lifetimes, typically more than a year, while utilizing constant-magnitude low-thrust, with a characteristic on-off profile. A cooperative guidance law capable of cluster establishment and maintenance under realistic environ- mental perturbations is developed. The guidance law is optimized for fuel consumption, subject to relative distance constraints. Some of the solutions found to the optimal guidance problem require only a single maneuver arc to keep the cluster within relatively close distances for an entire year

Gauge Theory for Finite-Dimensional Dynamical Systems

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems with implications to numerical integration of differential equations. We distinguish between rescriptive and descriptive gauge symmetry. Rescriptive gauge symmetry is, in essence, re-scaling of the independent variable, while descriptive gauge symmetry is a Yang-Mills-like transformation of the velocity vector field, adapted to finite-dimensional systems. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently "disordered" flow into a regular dynamical process, and that there exists a remarkable connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse engineering and scientific fields, including quantum mechanics, chemistry, rigid-body dynamics and information theory

Periodic Corrections in Secular Milankovitch Theory Applied to Passive Debris Removal

International audienceMost cartographic stability maps advocated for use in the new passive debris removal ideology based on orbital resonances are obtained through crude averaging methods. This means that from an operational perspective, its not clear where in the osculating space one should actually target to place the satellite on a natural disposal trajectory. It is also not obvious what effects the short-periodic terms may have on these re-entry solutions. We will derive the periodic corrections terms for the dominant perturbations affecting Earth satellites and investigate these considerations

A hybrid multiagent approach for global trajectory optimization

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers(corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods

Nonsingular vectorial reformulation of the short-period corrections in Kozai’s oblateness solution

International audienceWe derive a new analytical solution for the first-order, short-periodic perturbations due to planetary oblateness and systematically compare our results to the classical Brouwer–Lyddane transformation. Our approach is based on the Milankovitch vectorial elements and is free of all the mathematical singularities. Being a non-canonical set, our derivation follows the scheme used by Kozai in his oblateness solution. We adopt the mean longitude as the fast variable and present a compact power-series solution in eccentricity for its short-periodic perturbations that relies on Hansen’s coefficients. We also use a numerical averaging algorithm based on the fast-Fourier transform to further validate our new mean-to-osculating and inverse transformations. This technique constitutes a new approach for deriving short-periodic corrections and exhibits performance that are comparable to other existing and well-established theories, with the advantage that it can be potentially extended to modeling non-conservative orbit perturbations

Periodic Corrections in Secular Milankovitch Theory Applied to Passive Debris Removal

International audienceMost cartographic stability maps advocated for use in the new passive debris removal ideology based on orbital resonances are obtained through crude averaging methods. This means that from an operational perspective, its not clear where in the osculating space one should actually target to place the satellite on a natural disposal trajectory. It is also not obvious what effects the short-periodic terms may have on these re-entry solutions. We will derive the periodic corrections terms for the dominant perturbations affecting Earth satellites and investigate these considerations

Long-term evolution of orbits about a precessing oblate planet. 3. A semianalytical and a purely numerical approach

Construction of a theory of orbits about a precessing oblate planet, in terms of osculating elements defined in a frame of the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2005, 2006). We now combine that analytical machinery with numerics. The resulting semianalytical theory is then applied to Deimos over long time scales. In parallel, we carry out a purely numerical integration in an inertial Cartesian frame. The results agree to within a small margin, for over 10 Myr, demonstrating the applicability of our semianalytical model over long timescales. This will enable us to employ it at the further steps of the project, enriching the model with the tides, the pull of the Sun, and the planet's triaxiality. Another goal of our work was to check if the equinoctial precession predicted for a rigid Mars could have been sufficient to repel the orbits away from the equator. We show that for low initial inclinations, the orbit inclination reckoned from the precessing equator of date is subject only to small variations. This is an extension, to non-uniform precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession and a low initial inclination. However, near-polar initial inclinations may exhibit considerable variations for up to +/- 10 deg in magnitude. Nevertheless, the analysis confirms that an oblate planet can, indeed, afford large variations of the equinoctial precession over hundreds of millions of years, without repelling its near-equatorial satellites away from the equator of date: the satellite inclination oscillates but does not show a secular increase. Nor does it show secular decrease, a fact that is relevant to the discussion of the possibility of high-inclination capture of Phobos and Deimos