103 research outputs found
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
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
Tidal torques. A critical review of some techniques
We point out that the MacDonald formula for body-tide torques is valid only
in the zeroth order of e/Q, while its time-average is valid in the first order.
So the formula cannot be used for analysis in higher orders of e/Q. This
necessitates corrections in the theory of tidal despinning and libration
damping.
We prove that when the inclination is low and phase lags are linear in
frequency, the Kaula series is equivalent to a corrected version of the
MacDonald method. The correction to MacDonald's approach would be to set the
phase lag of the integral bulge proportional to the instantaneous frequency.
The equivalence of descriptions gets violated by a nonlinear
frequency-dependence of the lag.
We explain that both the MacDonald- and Darwin-torque-based derivations of
the popular formula for the tidal despinning rate are limited to low
inclinations and to the phase lags being linear in frequency. The
Darwin-torque-based derivation, though, is general enough to accommodate both a
finite inclination and the actual rheology.
Although rheologies with Q scaling as the frequency to a positive power make
the torque diverge at a zero frequency, this reveals not the impossible nature
of the rheology, but a flaw in mathematics, i.e., a common misassumption that
damping merely provides lags to the terms of the Fourier series for the tidal
potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the
magnitudes of the terms, too, get changed. Reinstating of this detail tames the
infinities and rehabilitates the "impossible" scaling law (which happens to be
the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial
text overlap with arXiv:0712.105
Newton-Hooke type symmetry of anisotropic oscillators
The rotation-less Newton--Hooke - type symmetry found recently in the Hill
problem and instrumental for explaining the center-of-mass decomposition is
generalized to an arbitrary anisotropic oscillator in the plane. Conversely,
the latter system is shown, by the orbit method, to be the most general one
with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic
case. Star escape from a Galaxy is studied as application.Comment: Updated version with more figures added. 34 pages, 7 figures.
Dedicated to the memory of J.-M. Souriau, deceased on March 15 2012, at the
age of 9
The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion
The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO(3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface and the conjugate points of this metric are evaluated using recent work [4] on surfaces of revolution
The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations
This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body
dynamics and presents some new results. As is well known, the problem of
unsupported and unperturbed rigid rotator can be reduced. The availability of
this reduction is offered by the underlying symmetry, which stems from
conservation of the angular momentum and rotational kinetic energy. When a
perturbation is turned on, these quantities are no longer preserved.
Nonetheless, the language of reduced description remains extremely instrumental
even in the perturbed case. We describe the canonical reduction performed by
the Serret-Andoyer (SA) method, and discuss its applications to attitude
dynamics and to the theory of planetary rotation. Specifically, we consider the
case of angular-velocity-dependent torques, and discuss the
variation-of-parameters-inherent antinomy between canonicity and osculation.
Finally, we address the transformation of the Andoyer variables into the
action-angle ones, using the method of Sadov
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