15,387 research outputs found
A Corollary for Nonsmooth Systems
In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem
are presented for nonautonomous systems described by nonlinear differential
equations with discontinuous right-hand sides. Lyapunov-based analysis methods
are developed using differential inclusions to achieve asymptotic convergence
when the candidate Lyapunov derivative is upper bounded by a negative
semi-definite function
Swimming in curved space or The Baron and the cat
We study the swimming of non-relativistic deformable bodies in (empty) static
curved spaces. We focus on the case where the ambient geometry allows for rigid
body motions. In this case the swimming equations turn out to be geometric. For
a small swimmer, the swimming distance in one stroke is determined by the
Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure
Spin-squared Hamiltonian of next-to-leading order gravitational interaction
The static, i.e., linear momentum independent, part of the next-to-leading
order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the
post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz
for the Hamilton constraint. All coefficients in this ansatz can be uniquely
fixed for black holes. The resulting Hamiltonian fits into the canonical
formalism of Arnowitt, Deser, and Misner (ADM) and is given in their
transverse-traceless (ADMTT) gauge. This completes the recent result for the
momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary
black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for
BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of
motion resulting from this Hamiltonian are an important step toward more
accurate calculations of templates for gravitational waves.Comment: REVTeX4, 10 pages, v2: minor improvements in the presentation, v3:
added omission in Eq. (4) and corrected coefficients in the result, Eq. (9);
version to appear in Phys. Rev.
Materials and structures for hypersonic vehicles
Hypersonic vehicles are envisioned to require, in addition to carbon-carbon and ceramic-matrix composities for leading edges heated to above 2000 F, such 600 to 1800 F operating temperature materials as advanced Ti alloys, nickel aluminides, and metal-matrix composited; These possess the necessary low density and high strength and stiffness. The primary design drivers are maximum vehicle heating rate, total heat load, flight envelope, propulsion system type, mission life requirements and liquid hydrogen containment systems. Attention is presently given to aspects of these materials and structures requiring more intensive development
The grammatical status of "the same"
The same, consisting of two words (or of clinic-plus-word), functions as a single grammatical item. Basically, it belongs to the determiner slot in phrase structure (together with articles, demonstratives and possessors). Like demonstratives, it may function as a substitution anaphor. But the same also shares some properties with adjectives — it can make up a complete copula complement, it may be the first element of a reduced relative clause, it may be followed by a preposition plus NP, and it has limited function as an adverb
Spinning test particles and clock effect in Schwarzschild spacetime
We study the behaviour of spinning test particles in the Schwarzschild
spacetime. Using Mathisson-Papapetrou equations of motion we confine our
attention to spatially circular orbits and search for observable effects which
could eventually discriminate among the standard supplementary conditions
namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the
world line chosen for the multipole reduction and whose unit tangent we denote
as is a circular orbit then also the generalized momentum of the
spinning test particle is tangent to a circular orbit even though and
are not parallel four-vectors. These orbits are shown to exist because the spin
induced tidal forces provide the required acceleration no matter what
supplementary condition we select. Of course, in the limit of a small spin the
particle's orbit is close of being a circular geodesic and the (small)
deviation of the angular velocities from the geodesic values can be of an
arbitrary sign, corresponding to the possible spin-up and spin-down alignment
to the z-axis. When two spinning particles orbit around a gravitating source in
opposite directions, they make one loop with respect to a given static observer
with different arrival times. This difference is termed clock effect. We find
that a nonzero gravitomagnetic clock effect appears for oppositely orbiting
both spin-up or spin-down particles even in the Schwarzschild spacetime. This
allows us to establish a formal analogy with the case of (spin-less) geodesics
on the equatorial plane of the Kerr spacetime. This result can be verified
experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum
gravity, 200
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