5,272 research outputs found
Astrometric observations of comets and asteroids and subsequent orbital investigations
Comets and minor planets were observed with a 155 cm reflector. Their orbital positions are presented in tabular form
On the Size-Dependence of the Inclination Distribution of the Main Kuiper Belt
We present a new analysis of the currently available orbital elements for the
known Kuiper belt objects. In the non-resonant, main Kuiper belt we find a
statistically significant relationship between an object's absolute magnitude
(H) and its inclination (i). Objects with H~170 km for a 4%
albedo) have higher inclinations than those with H>6.5 (radii >~ 170 km). We
have shown that this relationship is not caused by any obvious observational
bias. We argue that the main Kuiper belt consists of the superposition of two
distinct distributions. One is dynamically hot with inclinations as large as
\~35 deg and absolute magnitudes as bright as 4.5; the other is dynamically
cold with i6.5. The dynamically cold population is most likely
dynamically primordial. We speculate on the potential causes of this
relationship.Comment: 14 pages, 6 postscript figure
The study of the physics of cometary nuclei
A semiannual progress report describing the work completed during the period 1 September 1975 to 29 February 1976 on the physics of cometary nuclei was given. The following items were discussed: (1) a paper entitled ""A speculation about comets and the earth'', (2) a chapter entitled"" The physics of comets'' for ""Reviews of Astronomy and Astrophysics'', (3) continuing work on split comets, and (4) results dealing with a new application of nongravitational solar-radial forces as a measure of comet nucleus dimensions and activity
Variational Principles for Lagrangian Averaged Fluid Dynamics
The Lagrangian average (LA) of the ideal fluid equations preserves their
transport structure. This transport structure is responsible for the Kelvin
circulation theorem of the LA flow and, hence, for its convection of potential
vorticity and its conservation of helicity.
Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational
framework that implies the LA fluid equations. This is expressed in the
Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated
for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure
Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications
We develop the necessary tools, including a notion of logarithmic derivative
for curves in homogeneous spaces, for deriving a general class of equations
including Euler-Poincar\'e equations on Lie groups and homogeneous spaces.
Orbit invariants play an important role in this context and we use these
invariants to prove global existence and uniqueness results for a class of PDE.
This class includes Euler-Poincar\'e equations that have not yet been
considered in the literature as well as integrable equations like Camassa-Holm,
Degasperis-Procesi, CH and DP equations, and the geodesic equations
with respect to right invariant Sobolev metrics on the group of diffeomorphisms
of the circle
Nonaffine Correlations in Random Elastic Media
Materials characterized by spatially homogeneous elastic moduli undergo
affine distortions when subjected to external stress at their boundaries, i.e.,
their displacements \uv (\xv) from a uniform reference state grow linearly
with position \xv, and their strains are spatially constant. Many materials,
including all macroscopically isotropic amorphous ones, have elastic moduli
that vary randomly with position, and they necessarily undergo nonaffine
distortions in response to external stress. We study general aspects of
nonaffine response and correlation using analytic calculations and numerical
simulations. We define nonaffine displacements \uv' (\xv) as the difference
between \uv (\xv) and affine displacements, and we investigate the
nonaffinity correlation function
and related functions. We introduce four model random systems with random
elastic moduli induced by locally random spring constants, by random
coordination number, by random stress, or by any combination of these. We show
analytically and numerically that scales as A |\xv|^{-(d-2)}
where the amplitude is proportional to the variance of local elastic moduli
regardless of the origin of their randomness. We show that the driving force
for nonaffine displacements is a spatial derivative of the random elastic
constant tensor times the constant affine strain. Random stress by itself does
not drive nonaffine response, though the randomness in elastic moduli it may
generate does. We study models with both short and long-range correlations in
random elastic moduli.Comment: 22 Pages, 18 figures, RevTeX
- …