21,400 research outputs found
Orbital dynamics of earth-orbiting 'smart dust' spacecraft under the effects of solar radiation pressure and aerodynamic drag
This paper investigates how the perturbations due to asymmetric solar radiation pressure, in presence of Earth's shadow, and atmospheric drag can be balanced to obtain long-lived Earth centered orbits for swarms of SpaceChips, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where a Sun-synchronous apse-line precession is achieved passively. The long-term evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Therefore, long-lived orbits can be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the short life-time of high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the end-of life decay of SpaceChips, thus preventing long-lived orbit debris
Orbit design for future SpaceChip swarm missions
The effect of solar radiation pressure and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is exploited to design long-lived orbits about the Earth. The orbit energy gain due to asymmetric solar radiation pressure, considering the Earth shadow, is used to balance the energy loss due to atmospheric drag. Future missions for a swarm of SpaceChips are proposed, where a number of small devices are released from a conventional spacecraft to perform spatially distributed measurements of the conditions in the ionosphere and exosphere. It is shown that the orbit lifetime can be extended and indeed selected through solar radiation pressure and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag
Orbit evolution, maintenance and disposal of SpaceChip swarms
The combined effect of solar radiation pressure and atmospheric drag is investigated for future mission conceptsfor swarms of satellites-on-a-chip (SpaceChips). The natural evolution of the swarm is exploited to perform spatially distributed measurements of the upper layers of the atmosphere. The energy gain from asymmetric solar radiation pressure can be used to balance the energy dissipation from atmospheric drag. An algorithm for long-term orbit control is then designed, based on changing the reflectivity coefficient of the SpaceChips. The subsequent modulation of the solar radiation pressure allows stabilisation of the swarm in the orbital element phase space. It is shown that the normally short orbit lifetime for such devices can be extended through the interaction of solar radiation pressure and atmospheric drag and indeed selected and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag
Orbit control of high area-to-mass ratio spacecraft using electrochromic coating
This paper presents a novel method for the orbit control of high area-to-mass ratio spacecraft, such as spacecraft-on-a-chip, future „smart dust‟ devices and inflatable spacecraft. By changing the reflectivity coefficient of an electrochromic coating of the spacecraft, the perturbing effect of solar radiation pressure (SRP) is exploited to enable long-lived orbits and to control formations, without the need for propellant consumption or active pointing. The spacecraft is coated with a thin film of an electrochromic material that changes its reflectivity coefficient when a small current is applied. The change of reflectance alters the fraction of the radiation pressure force that is transmitted to the satellite, and hence has a direct effect on the spacecraft orbit evolution. The orbital element space is analysed to identify orbits which can be stabilised with electrochromic orbit control. A closed-loop feedback control method using an artificial potential field approach is introduced to stabilise these otherwise unsteady orbits. The stability of this solution is analysed and verified through numerical simulation. Finally, a test case is simulated in which the control method is used to perform orbital manoeuvres for a spacecraft formation
Entire slice regular functions
Entire functions in one complex variable are extremely relevant in several
areas ranging from the study of convolution equations to special functions. An
analog of entire functions in the quaternionic setting can be defined in the
slice regular setting, a framework which includes polynomials and power series
of the quaternionic variable. In the first chapters of this work we introduce
and discuss the algebra and the analysis of slice regular functions. In
addition to offering a self-contained introduction to the theory of
slice-regular functions, these chapters also contain a few new results (for
example we complete the discussion on lower bounds for slice regular functions
initiated with the Ehrenpreis-Malgrange, by adding a brand new Cartan-type
theorem).
The core of the work is Chapter 5, where we study the growth of entire slice
regular functions, and we show how such growth is related to the coefficients
of the power series expansions that these functions have. It should be noted
that the proofs we offer are not simple reconstructions of the holomorphic
case. Indeed, the non-commutative setting creates a series of non-trivial
problems. Also the counting of the zeros is not trivial because of the presence
of spherical zeros which have infinite cardinality. We prove the analog of
Jensen and Carath\'eodory theorems in this setting
Single-species fragmentation: the role of density-dependent feedbacks
Internal feedbacks are commonly present in biological populations and can
play a crucial role in the emergence of collective behavior. We consider a
generalization of Fisher-KPP equation to describe the temporal evolution of the
distribution of a single-species population. This equation includes the
elementary processes of random motion, reproduction and, importantly, nonlocal
interspecific competition, which introduces a spatial scale of interaction.
Furthermore, we take into account feedback mechanisms in diffusion and growth
processes, mimicked through density-dependencies controlled by exponents
and , respectively. These feedbacks include, for instance, anomalous
diffusion, reaction to overcrowding or to rarefaction of the population, as
well as Allee-like effects. We report that, depending on the dynamics in place,
the population can self-organize splitting into disconnected sub-populations,
in the absence of environment constraints. Through extensive numerical
simulations, we investigate the temporal evolution and stationary features of
the population distribution in the one-dimensional case. We discuss the crucial
role that density-dependency has on pattern formation, particularly on
fragmentation, which can bring important consequences to processes such as
epidemic spread and speciation
Gravitational spectra from direct measurements
A simple rapid method is described for determining the spectrum of a surface field from harmonic analysis of direct measurements along great circle arcs. The method is shown to give excellent overall trends to very high degree from even a few short arcs of satellite data. Three examples are taken with perfect measurements of satellite tracking over a planet made up of hundreds of point-masses using (1) altimetric heights from a low orbiting spacecraft, (2) velocity residuals between a low and a high satellite in circular orbits, and (3) range-rate data between a station at infinity and a satellite in highly eccentric orbit. In particular, the smoothed spectrum of the Earth's gravitational field is determined to about degree 400(50 km half wavelength) from 1 D x 1 D gravimetry and the equivalent of 11 revolutions of Geos 3 and Skylab altimetry. This measurement shows there is about 46 cm of geoid height remaining in the field beyond degree 180
Regular Moebius transformations of the space of quaternions
Let H be the real algebra of quaternions. The notion of regular function of a
quaternionic variable recently presented by G. Gentili and D. C. Struppa
developed into a quite rich theory. Several properties of regular quaternionic
functions are analogous to those of holomorphic functions of one complex
variable, although the diversity of the quaternionic setting introduces new
phenomena. This paper studies regular quaternionic transformations. We first
find a quaternionic analog to the Casorati-Weierstrass theorem and prove that
all regular injective functions from H to itself are affine. In particular, the
group Aut(H) of biregular functions on H coincides with the group of regular
affine transformations. Inspired by the classical quaternionic linear
fractional transformations, we define the regular fractional transformations.
We then show that each regular injective function from the Alexandroff
compactification of H to itself is a regular fractional transformation.
Finally, we study regular Moebius transformations, which map the unit ball B
onto itself. All regular bijections from B to itself prove to be regular
Moebius transformations.Comment: 12 page
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