129 research outputs found
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
New exact analytic solutions are introduced for the rotational motion of a
rigid body having two equal principal moments of inertia and subjected to an
external torque which is constant in magnitude. In particular, the solutions
are obtained for the following cases: (1) Torque parallel to the symmetry axis
and arbitrary initial angular velocity; (2) Torque perpendicular to the
symmetry axis and such that the torque is rotating at a constant rate about the
symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial
angular velocity perpendicular to the symmetry axis, with the torque being
fixed with the body. In addition to the solutions for these three forced cases,
an original solution is introduced for the case of torque-free motion, which is
simpler than the classical solution as regards its derivation and uses the
rotation matrix in order to describe the body orientation. This paper builds
upon the recently discovered exact solution for the motion of a rigid body with
a spherical ellipsoid of inertia. In particular, by following Hestenes' theory,
the rotational motion of an axially symmetric rigid body is seen at any instant
in time as the combination of the motion of a "virtual" spherical body with
respect to the inertial frame and the motion of the axially symmetric body with
respect to this "virtual" body. The kinematic solutions are presented in terms
of the rotation matrix. The newly found exact analytic solutions are valid for
any motion time length and rotation amplitude. The present paper adds further
elements to the small set of special cases for which an exact solution of the
rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The
following typos present in the Journal version are HERE corrected: 1)
Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3)
Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6
Condensing Momentum Modes in 2-d 0A String Theory with Flux
We use a combination of conformal perturbation theory techniques and matrix
model results to study the effects of perturbing by momentum modes two
dimensional type 0A strings with non-vanishing Ramond-Ramond (RR) flux. In the
limit of large RR flux (equivalently, mu=0) we find an explicit analytic form
of the genus zero partition function in terms of the RR flux and the
momentum modes coupling constant alpha. The analyticity of the partition
function enables us to go beyond the perturbative regime and, for alpha>> q,
obtain the partition function in a background corresponding to the momentum
modes condensation. For momenta such that 0<p<2 we find no obstruction to
condensing the momentum modes in the phase diagram of the partition function.Comment: 22 page
I.B.S. coatings on large substrates: Towards an improvement of the mechanical and optical performances
présenté par A. RemillieuxLarge mirrors (350 mm), having extremely low optical loss (absorption, scattering, wavefront) were coated for the VIRGO interferometer. The new mirror generation needs better wavefront and lower mechanical loss. The first results are discussed
Original optical metrologies of large components
présentée par A. RemillieuxThe coating deposition on large optical components (diameter 350 mm) has required the development of new metrology tools at 1064 nm. To give realistic values of the optical performances, the whole surface of the component needs to be scanned. Our scatterometer (commercial system) has been upgraded to support large and heavy samples. The other metrology tools are prototypes we have developed. We can mention the absorption (photothermal effect) and birefringence bench, a control interferometer equipped with an original stitching option, the optical profilometer (RMS roughness and small defect measurements). A detailed description of these metrology benches will be exposed. Their sensitivity, accuracy and capability to map the optical properties of substrates or mirrors will be discussed. We will describe the recent developments: the stitching option adapted to the Micromap profilometer to measure the RMS roughness on larger area (exploration of a new spatial frequency domain), the accurate bulk absorption calibration
A Laser Frequency Comb System for Absolute Calibration of the VTT Echelle Spectrograph
A wavelength calibration system based on a laser frequency comb (LFC) was
developed in a co-operation between the Kiepenheuer-Institut f\"ur
Sonnenphysik, Freiburg, Germany and the Max-Planck-Institut f\"ur Quantenoptik,
Garching, Germany for permanent installation at the German Vacuum Tower
Telescope (VTT) on Tenerife, Canary Islands. The system was installed
successfully in October 2011. By simultaneously recording the spectra from the
Sun and the LFC, for each exposure a calibration curve can be derived from the
known frequencies of the comb modes that is suitable for absolute calibration
at the meters per second level. We briefly summarize some topics in solar
physics that benefit from absolute spectroscopy and point out the advantages of
LFC compared to traditional calibration techniques. We also sketch the basic
setup of the VTT calibration system and its integration with the existing
echelle spectrograph.Comment: 9 pages, 2 figures; Solar Physics 277 (2012
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
High-contrast imaging constraints on gas giant planet formation - The Herbig Ae/Be star opportunity
Planet formation studies are often focused on solar-type stars, implicitly
considering our Sun as reference point. This approach overlooks, however, that
Herbig Ae/Be stars are in some sense much better targets to study planet
formation processes empirically, with their disks generally being larger,
brighter and simply easier to observe across a large wavelength range. In
addition, massive gas giant planets have been found on wide orbits around early
type stars, triggering the question if these objects did indeed form there and,
if so, by what process. In the following I briefly review what we currently
know about the occurrence rate of planets around intermediate mass stars,
before discussing recent results from Herbig Ae/Be stars in the context of
planet formation. The main emphasis is put on spatially resolved polarized
light images of potentially planet forming disks and how these images - in
combination with other data - can be used to empirically constrain (parts of)
the planet formation process. Of particular interest are two objects, HD100546
and HD169142, where, in addition to intriguing morphological structures in the
disks, direct observational evidence for (very) young planets has been
reported. I conclude with an outlook, what further progress we can expect in
the very near future with the next generation of high-contrast imagers at 8-m
class telescopes and their synergies with ALMA.Comment: Accepted by Astrophysics and Space Science as invited short review in
special issue about Herbig Ae/Be stars; 12 pages incl. 5 figures, 2 tables
and reference
Against all odds? Forming the planet of the HD196885 binary
HD196885Ab is the most "extreme" planet-in-a-binary discovered to date, whose
orbit places it at the limit for orbital stability. The presence of a planet in
such a highly perturbed region poses a clear challenge to planet-formation
scenarios. We investigate this issue by focusing on the planet-formation stage
that is arguably the most sensitive to binary perturbations: the mutual
accretion of kilometre-sized planetesimals. To this effect we numerically
estimate the impact velocities amongst a population of circumprimary
planetesimals. We find that most of the circumprimary disc is strongly hostile
to planetesimal accretion, especially the region around 2.6AU (the planet's
location) where binary perturbations induce planetesimal-shattering of
more than 1km/s. Possible solutions to the paradox of having a planet in such
accretion-hostile regions are 1) that initial planetesimals were very big, at
least 250km, 2) that the binary had an initial orbit at least twice the present
one, and was later compacted due to early stellar encounters, 3) that
planetesimals did not grow by mutual impacts but by sweeping of dust (the
"snowball" growth mode identified by Xie et al., 2010b), or 4) that HD196885Ab
was formed not by core-accretion but by the concurent disc instability
mechanism. All of these 4 scenarios remain however highly conjectural.Comment: accepted for publication by Celestial Mechanics and Dynamical
Astronomy (Special issue on EXOPLANETS
Influence of synthesis and processing parameters of the columbite precursor on the amount of Perovskite PMN
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