9,143 research outputs found
Synchronization of Huygens' clocks and the Poincare method
We study two models of connected pendulum clocks synchronizing their
oscillations, a phenomenon originally observed by Huygens. The oscillation
angles are assumed to be small so that the pendulums are modeled by harmonic
oscillators, clock escapements are modeled by the van der Pol terms. The mass
ratio of the pendulum bobs to their casings is taken as a small parameter.
Analytic conditions for existence and stability of synchronization regimes, and
analytic expressions for their stable amplitudes and period corrections are
derived using the Poincare theorem on existence of periodic solutions in
autonomous quasi-linear systems. The anti-phase regime always exists and is
stable under variation of the system parameters. The in-phase regime may exist
and be stable, exist and be unstable, or not exist at all depending on
parameter values. As the damping in the frame connecting the clocks is
increased the in-phase stable amplitude and period are decreasing until the
regime first destabilizes and then disappears. The results are most complete
for the traditional three degrees of freedom model, where the clock casings and
the frame are consolidated into a single mass.Comment: 23 pages, 8 figure
Self-synchronization and controlled synchronization
An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give
Conveyor belt clock synchronization
A protocol for synchronizing distant clocks is proposed that does not rely on
the arrival times of the signals which are exchanged, and an optical
implementation based on coherent-state pulses is described. This protocol is
not limited by any dispersion that may be present in the propagation medium
through which the light signals are exchanged. Possible improvements deriving
from the use of quantum-mechanical effects are also addressed.Comment: 8 pages, 7 figure
A relativistic analysis of clock synchronization
The relativistic conversion between coordinate time and atomic time is reformulated to allow simpler time calculations relating analysis in solar-system barycentric coordinates (using coordinate time) with earth-fixed observations (measuring earth-bound proper time or atomic time.) After an interpretation of terms, this simplified formulation, which has a rate accuracy of about 10 to the minus 15th power, is used to explain the conventions required in the synchronization of a world wide clock network and to analyze two synchronization techniques-portable clocks and radio interferometry. Finally, pertinent experiment tests of relativity are briefly discussed in terms of the reformulated time conversion
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