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In order to address the issue of quantitatively solving the impact of perturbation forces and initial errors on rendezvous accuracy, traditional analytical methods are not suitable, and the calculation steps for statistical methods based on Monte Carlo simulation analysis are complex and computationally time-consuming. To overcome these challenges, this paper proposes a method for analysing rendezvous accuracy based on an improved relative motion dynamics model. Describing the relative motion between a sub-spacecraft and a target spacecraft by an improved Clohessy-Wiltshire (C-W) equation. By employing the derived state transition matrix from the model, it is possible to calculate the error propagation during the rendezvous process and express the rendezvous accuracy analytically. Through simulation examples, the proposed method proves to be both accurate and efficient in analysing the influence of perturbation forces and random errors such as initial position and velocity on rendezvous accuracy. This study verifies the correctness and effectiveness of the approach.

To increase the interferometric measurement resolution in the Taiji program, we present a noise suppression method in this paper. Taking the specific micro-force perturbation and temperature fluctuation in the Taiji-1 interferometer as an example, we set up and experimentally verified the corresponding transfer function to quantify the effect of both noise sources on the interferometric results. Consistent results were obtained between the numerical and experimental results for the transfer function. It is instructive to eliminate the micro-force perturbations and temperature fluctuations during on-orbit interferometric measurement for as long as the acquisition of the force or temperature distribution of related surfaces and the corresponding transfer functions. This indicates that the method can be used for noise sensing and more in the field of noise elimination and measurement resolution improvement for future Taiji program interferometers.

This study aims to numerically investigate a transonic compressor by solving the unsteady Reynolds-averaged Navier–Stokes equations. The flow mechanisms related to unsteady flow were carefully examined and compared between rotors with non-uniform tip clearance (D1) and small-value tip clearance (P1). The unsteady flow field near the 50% and 95% blade span characterized by unsteady rotor–stator interaction was analyzed in detail for near-stall (NS) conditions. According to the findings, the perturbation of unsteady aerodynamic force for the stator is much bigger than that of the rotor. At the mid-gap between the rotor and stator, the perturbation of tangential velocity of the D1 scheme in the rotor and stator frame is reduced. At the rotor’s outlet region, the perturbation intensity is divided into three main perturbation regions, which are respectively concentrated in the TLV near the upper endwall, the corner separation at the blade root, and the wake of the whole blade span. Through the analysis of the wake transportation characteristics, it was found that when the wake passes through the stator blade surface, the wake exerts a substantial influence on the flow within the stator passage. It further leads to notable pressure perturbations on the stator’s surface, as well as affecting the development and flow loss of the boundary layer. The negative jet effect induces opposite secondary flow velocity on both sides of the wake near the stator’s surfaces. Therefore, the velocity at a specific point on the stator’s suction surface will decrease and then increase. Conversely, the velocity at a particular point on the pressure surface will increase and then decrease.

One of the most valuable regions for telecommunication and space science is the geostationary earth orbit (GEO). On 27 November 2019, Egypt successfully launched its telecommunications satellite TIBA-1 into space. This paper aims to effectively identify and concurrently track this satellite from our Kottamia observatory station, National Research Institute of Astronomy and Geophysics (NRIAG) - Egypt. The images of the satellite are processed by the Apex II astronomical image processing package to obtain optical measurements, the apparent magnitude, and the phase angle. The initial orbit of the TIBA-1 satellite is determined using angle-only optical measurements for 4 months. The Double-r iteration method is used to determine the state distance vectors for orbital elements under different perturbation forces. Then, the results are compared with the positions predicted using the North American Aerospace Defense Command (NORAD) reference catalog.

The electronic absorption spectra of acridine and 9-aminoacridine have been studied in various fluid solutions at room temperature. The modified Onsager–Abe–Iweibo reaction field model for a spherical molecule was employed to determine the oscillator strength, f, in vapour phase. The intensity enhancements for the forbidden transition observed are ascribed to perturbation forces between the solute and solvent molecules.

Many studies have reported postural control against support surface translation. However, postural control mechanism against external force perturbation is not clear. Therefore, in this study we investigated the postural recovery against external force (1∼4Kg) applied to the high-back in health young male subjects (24±4 years). Kinematic data and center of pressure of the reaction to an unexpected perturbation were analyzed. Experimental results showed that the hill-lifting strategy with ankle plantarflexion and knee hyperextension was used in all subjects, regardless of the force magnitude. Specifically, maximum ankle plantarflexion and hip flexion increased with the perturbation force magnitude, the heel vertical excursion and anterior COP excursion. The results of this study show that the postural control strategy for the external force perturbation is quite different from that for surface translation and needs further investigation.

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting Green’s function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.

We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers ( $\\mathit{Re}$ ). At high $\\mathit{Re}$ , when inertia dominates the impact processes, we show that the early time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high $\\mathit{Re}$ . When viscous forces gradually set in with decreasing $\\mathit{Re}$ , we analyse the early time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing $\\mathit{Re}$ . Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high $\\mathit{Re}$ following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high $\\mathit{Re}$ . The limit of the self-similar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop-impact processes.

Existing experimental studies on human balance have primarily focused on biomechanical responses of major lower-limb joints, while the role of hallux and lesser toes of human foot in response to external perturbations has not been fully explored. Although toe grip strength may significantly influence balance performance, a more physiological-relevant toe grip evaluation, has not yet been established. This study investigates the biomechanical grip strength of the hallux and lesser toes during perturbations by quantifying the shear interactions (i.e., horizontal traction forces) at the foot–ground interface. A robotic platform with an instrumented multi-axial force platform was employed to analyze the involvement of the hallux and lesser toes in maintaining standing balance due to random ground perturbations. Our results indicate that hallux and lesser toes demonstrated significant direction-specific shear responses, and the proportion of shear traction force in the hallux and lesser toes significantly increased, particularly for perturbations in the posterior half-plane (p < 0.05). A substantial increase in shear traction force underneath the lesser toes was observed during contralateral perturbation events (p < 0.05). Importantly, the lesser toes could generate substantial shear traction forces by enhancing griping following perturbation, a capability not shown in other foot regions. This study introduced a novel approach for precisely quantifying the grip functions of individual toes at in-vivo perturbing conditions. The information provided is envisaged to have important implications on improved interventions for posture and balance rehabilitation.