186 research outputs found
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
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