Transitory second-order reciprocal connection for two surfaces in point contact

This paper investigates the instantaneous spatial higher pair to lower pair substitute-connection which is kinematically equivalent up to acceleration analysis for two smooth surfaces in point contact. The existing first-order equivalent substitute-connection consisting of a Hooke's joint (U-joint) and a spherical joint (S-joint) connected by an additional link is extended up to second-order. A two step procedure is chalked out for achieving this equivalence. First, the existing method is employed for velocity equivalence. In the second step, the two centers of substitution are obtained as a conjugate relationship involving the principal normal curvatures of the surfaces at the contact point and the screw coordinates of the instantaneous screw axis (ISA) of the first-order relative motion. Unlike the classical planar replacement, this particular substitution cannot be done by merely examining the profiles of the contacting surfaces. An illustrative example of a three-link direct-contact mechanism is presented. (C) 2014 Elsevier Ltd. All rights reserved.

Micro-satellite angular rate estimation using second-order sliding mode observer

Development of computationally efficient and accurate attitude rate estimation algorithm using low-cost commercially available star sensor arrays and processing unit for micro-satellite mission is presented. Our design reduces the computational load of least square (LS)-based rate estimation method while maintaining the same accuracy compared to other rate estimation approaches. Furthermore, rate estimation accuracy is improved by using recently developed fast and accurate second-order sliding mode observer (SOSMO) scheme. It also gives robust estimation in the presence of modeling uncertainties, unknown disturbances, and measurement noise. Simulation study shows that rate estimation accuracy achieved by our LS-based method is comparable with other methods for a typical commercially available star sensor array. The robustness analysis of SOSMO with respect to measurement noise is also presented in this paper. Simulation test bench for a practical scenario of satellite rate estimation uses moment-of-inertia variation and environmental disturbances affecting a typical micro-satellite at 500km circular orbit. Comparison studies of SOSMO with 1-SMO and pseudo-linear Kalman filter show that satisfactory estimation accuracy is achieved by SOSMO.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Damping and saturation of a second order electron plasma wave echo

A description is given of experimental work on the damping of a second order electron plasma wave echo due to velocity space diffusion in a low temperature magnetoplasma. Sufficient precision was obtained to verify the theoretically predicted cubic rather than quadratic or quartic dependence of the damping on exciter separation. Compared to the damping predicted for Coulomb collisions in a thermal plasma in an infinite magnetic field, the magnitude of the damping was approximately as predicted, while the velocity dependence of the damping was weaker than predicted. The discrepancy is consistent with the actual non-Maxwellian electron distribution of the plasma.

In conjunction with the damping work, echo amplitude saturation was measured as a function of the velocity of the electrons contributing to the echo. Good agreement was obtained with the predicted J₁ Bessel function amplitude dependence, as well as a demonstration that saturation did not influence the damping results.

The effect of the group delay ripple of chirped fiber grating on composite second-order in optical fiber CATV system

The effect of group delay ripple of chirped fiber gratings on composite second-order (CSO) performance in optical fiber CATV system is investigated. We analyze the system CSO performances for different ripple amplitudes, periods and residual dispersion amounts in detail. It is found that the large ripple amplitude and small ripple period will deteriorate the system CSO performance seriously. Additionally, the residual dispersion amount has considerable effect on CSO performance in the case of small ripple amplitude and large ripple period. (c) 2004 Elsevier B.V. All rights reserved.

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Analysis of a second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer

A novel second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer (SRRSI) is proposed, and its filtering characteristics are investigated. By using birefringence in waveguide, a single ring resonator can be used to synthesize a filter with second-order response. Analytical formulas are derived for characteristics of the SRRSI varied with waveguide parameters.. such as the coupling coefficient; and the critical condition of a second-order Butterworth filter is given. The influence of loss in the ring resonator is also analyzed. (c) 2005 Elsevier B.V. All rights reserved.

Modelling and simulation of the second-order Doppler error of a laser dual-frequency interferometer

Only the first- order Doppler frequency shift is considered in current laser dual- frequency interferometers; however; the second- order Doppler frequency shift should be considered when the measurement corner cube ( MCC) moves at high velocity or variable velocity because it can cause considerable error. The influence of the second- order Doppler frequency shift on interferometer error is studied in this paper, and a model of the second- order Doppler error is put forward. Moreover, the model has been simulated with both high velocity and variable velocity motion. The simulated results show that the second- order Doppler error is proportional to the velocity of the MCC when it moves with uniform motion and the measured displacement is certain. When the MCC moves with variable motion, the second- order Doppler error concerns not only velocity but also acceleration. When muzzle velocity is zero the second- order Doppler error caused by an acceleration of 0.6g can be up to 2.5 nm in 0.4 s, which is not negligible in nanometric measurement. Moreover, when the muzzle velocity is nonzero, the accelerated motion may result in a greater error and decelerated motion may result in a smaller error.