2,283 research outputs found
Shape Control for Experimental Continuation
An experimental method has been developed to locate unstable equilibria of
nonlinear structures quasi-statically. The technique involves loading a
structure by application of either a force or a displacement at a main
actuation point, while simultaneously controlling the overall shape using
additional probe points. The method is applied to a shallow arch, and unstable
segments of its equilibrium path are identified experimentally for the first
time. Shape control is a fundamental building block for the experimental---as
opposed to numerical---continuation of nonlinear structures, which will
significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor
for linear transducer. Updated Figure 6 finite element results with correct
load multiplier for half-model. Updated paper text to reflect these changes.
5 pages, 6 figure
The non-resonant, relativistic dynamics of circumbinary planets
We investigate the non-resonant, 3-D (spatial) model of the hierarchical
system composed of point-mass stellar (or sub-stellar) binary and a low-mass
companion (a circumbinary planet or a brown dwarf). We take into account the
leading relativistic corrections to the Newtonian gravity. The secular model of
the system relies on the expansion of the perturbing Hamiltonian in terms of
the ratio of semi-major axes , averaged over the mean anomalies. We
found that the low-mass object in a distant orbit may excite large eccentricity
of the inner binary when the mutual inclination of the orbits is larger than
about of 60 deg. This is related to strong instability caused by a phenomenon
which acts similarly to the Lidov-Kozai resonance (LKR). The secular system may
be strongly chaotic and its dynamics unpredictable over the long-term time
scale. Our study shows that in the Jupiter-- or brown dwarf-- mass regime of
the low-massive companion, the restricted model does not properly describe the
long-term dynamics in the vicinity of the LKR. The relativistic correction is
significant for the parametric structure of a few families of stationary
solutions in this problem, in particular, for the direct orbits configurations
(with the mutual inclination less than 90 degrees). We found that the dynamics
of hierarchical systems with small may be qualitatively
different in the realm of the Newtonian (classic) and relativistic models. This
holds true even for relatively large masses of the secondaries.Comment: 18 pages, 17 figures, accepted to Monthly Notices of the Royal
Astronomical Societ
Spin-orbit coupling and chaotic rotation for coorbital bodies in quasi-circular orbits
Coorbital bodies are observed around the Sun sharing their orbits with the
planets, but also in some pairs of satellites around Saturn. The existence of
coorbital planets around other stars has also been proposed. For close-in
planets and satellites, the rotation slowly evolves due to dissipative tidal
effects until some kind of equilibrium is reached. When the orbits are nearly
circular, the rotation period is believed to always end synchronous with the
orbital period. Here we demonstrate that for coorbital bodies in quasi-circular
orbits, stable non-synchronous rotation is possible for a wide range of mass
ratios and body shapes. We show the existence of an entirely new family of
spin-orbit resonances at the frequencies , where is the
orbital mean motion, the orbital libration frequency, and an integer.
In addition, when the natural rotational libration frequency due to the axial
asymmetry, , has the same magnitude as , the rotation becomes
chaotic. Saturn coorbital satellites are synchronous since , but
coorbital exoplanets may present non-synchronous or chaotic rotation. Our
results prove that the spin dynamics of a body cannot be dissociated from its
orbital environment. We further anticipate that a similar mechanism may affect
the rotation of bodies in any mean-motion resonance.Comment: 6 pages. Astrophysical Journal (2013) 6p
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic
cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known
to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various
phase space variables, but details of the mechanisms underlying the complicated dynamics have
not previously been investigated. We identify global bifurcations that induce the onset of chaotic
dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis
of approximate return maps, locate the global bifurcations in parameter space. We find there is a
threshold in the size of certain symmetry-breaking terms below which there can be no persistent
switching. Our results are illustrated by a numerical example
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