scholarly journals Five-body choreography on the algebraic lemniscate is a potential motion

2019 ◽  
Vol 383 (15) ◽  
pp. 1711-1715
Author(s):  
Juan Carlos Lopez Vieyra
Keyword(s):  
Potential Motion

Surface waves on shear currents: solution of the boundary-value problem

1993 ◽  
Vol 252 ◽  
pp. 565-584 ◽  
Author(s):  
Victor I. Shrira
Keyword(s):  
Boundary Value Problem ◽  
Growth Rates ◽  
Wave Motion ◽  
Boundary Value ◽  
A Priori ◽  
Approximate Solutions ◽  
Short Wave ◽  
Capillary Waves ◽  
Potential Motion ◽  
Approximate Expressions

We consider a classic boundary-value problem for deep-water gravity-capillary waves in a shear flow, composed of the Rayleigh equation and the standard linearized kinematic and dynamic inviscid boundary conditions at the free surface. We derived the exact solution for this problem in terms of an infinite series in powers of a certain parameter e, which characterizes the smallness of the deviation of the wave motion from the potential motion. For the existence and absolute convergence of the solution it is sufficient that e be less than unity.The truncated sums of the series provide approximate solutions with a priori prescribed accuracy. In particular, for the short-wave instability, which can be interpreted as the Miles critical-layer-type instability, the explicit approximate expressions for the growth rates are derived. The growth rates in a certain (very narrow) range of scales can exceed the Miles increments caused by the wind.The effect of thin boundary layers on the dispersion relation was also investigated using an asymptotic procedure based on the smallness of the product of the layer thickness and wavenumber. The criterion specifying when and with what accuracy the boundary-layer influence can be neglected has been derived.

scholarly journals Motion of an infinite elliptic cylinder in fluids with constant vorticity

1937 ◽  
Vol 158 (895) ◽  
pp. 522-535 ◽  
Keyword(s):  
Equations Of Motion ◽  
Elliptic Cylinder ◽  
The Body ◽  
Uniform Rotation ◽  
Constant Vorticity ◽  
Uniform Shear ◽  
Potential Motion ◽  
Irrotational Motion ◽  
Shear Motion ◽  
Solid Bodies

An extension of Kirchoff’s theory of the motion of solid bodies in irrotationally moving liquids to the case of motion in liquids in which a vorticity is present does not exist. Only a few isolated cases of such motion are known. Bearing on the consideration of this paper, there is an important work by Taylor which expresses the additional pressure effect on a system of cylinders moving in a perfect liquid without rotation when the whole system is rotated uniformly about an axis. Taylor’s theory reduces the problem of such motion to one of irrotational motion. In the present paper the motion of a perfect liquid having constant vorticity, and in which a cylinder of any cross-section is moving in any manner, has been considered. The pressure integral can be obtained in a simple form, referred to axes fixed in the body, which is very suitable for calculation. It is shown, whenever the pure potential motion of the liquid for the rotation of the cylinder and the solution of a definite potential problem or the corresponding Green’s function can be found, the formula can be applied to calculate the motion of the cylinder in liquids with constant vorticity. Two important cases of constant vorticity are uniform shear motion along a direction and uniform rotation about an axis. In the present paper the former case is considered in detail for an elliptic cylinder. The case of uniform rotation being covered by Taylor’s result it is only verified that the present method gives the same result as Taylor’s formulae. There are some simple free motions of an elliptic cylinder in a liquid with uniform shear motion which have been discussed in the paper. 2—Equations of Motion Referred to Axes Fixed in the Body and the Pressure Integral It is first necessary to write down the equations of motion referred to a system of axes fixed in the body having both translation and rotation. These equations are obtained below following a method of Taylor.

scholarly journals LEARNING MAPS FOR OBJECT LOCALIZATION USING VISUAL-INERTIAL ODOMETRY

2020 ◽  
Vol V-1-2020 ◽  
pp. 343-350
Author(s):  
B. Zha ◽  
A. Yilmaz
Keyword(s):  
Object Motion ◽  
Spatial Uncertainty ◽  
Object Localization ◽  
Abstract Objects ◽  
Motion Patterns ◽  
Localization Accuracy ◽  
Single Location ◽  
Trajectory Classification ◽  
Potential Motion ◽  
Localization Approach

Abstract. Objects follow designated path on maps, such as vehicles travelling on a road. This observation signifies topological representation of objects’ motion on the map. Considering the position of object is unknown initially, as it traverses the map by moving and turning, the spatial uncertainty of its whereabouts reduces to a single location as the motion trajectory would fit only to a certain map trajectory. Inspired by this observation, we propose a novel end-to-end localization approach based on topological maps that exploits the object motion and learning the map using an recurrent neural network (RNN) model. The core of the proposed method is to learn potential motion patterns from the map and perform trajectory classification in the map’s edge-space. Two different trajectory representations, namely angle representation and augmented angle representation (incorporates distance traversed) are considered and an RNN is trained from the map for each representation to compare their performances. The localization accuracy in the tested map for the angle and augmented angle representations are 90.43% and 96.22% respectively. The results from the actual visual-inertial odometry have shown that the proposed approach is able to learn the map and localize objects based on their motion.

scholarly journals The Method of Pose Judgment of Potential Motion Damage in 3D Image Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Liping Gao
Keyword(s):  
Image Analysis ◽  
Small Sample Size ◽  
Image Data ◽  
Small Sample ◽  
3D Image ◽  
3D Image Analysis ◽  
Damage Degree ◽  
Damage Data ◽  
Potential Motion ◽  
Simulation Parameters

Objective. This work aimed to study the posture judgment method of 3D image analysis of potential motion damage. Methods. The motion damage collection was implemented by the 3D image analysis method, and 3D image data were adopted to identify the motion damage data. Moreover, 3D image acquisition technology was adopted to analyze the model of potential motion damage and analyze the simulation judgment result of potential motion damage. Specifically, it included simulation parameters, motion damage posture collection effect, damage detection speed at the collection point, damage accuracy, and damage degree. Results. (1) The analysis of the damage monitoring speed at multiple collection points of the athletes in the sports environment confirmed that the range of changes in different time periods was different, and the changes showed a fast to slow to fast trend. (2) The 3D image analysis had high accuracy in analyzing the posture of potential motion damage, which rationalized the evolution of injuries. (3) The degree of motion damage under a 3D image changed from rising to gradual, which was in line with the theoretical results (all p < 0.05). Conclusion. 3D image analysis can collect a high degree of small-sample-size data, then perform specific analysis, judgment, and summary, and finally, obtain objective and reasonable data. It greatly reduced the risk of potential motion damage for athletes and also improved the efficiency of injury recognition. Moreover, it reduced the chances of blind prevention and error prevention by athletes, thereby avoiding waste of resources. The simulation test confirmed the advantages of 3D image data collection in the sports environment, and it was solved that the current athletes cannot accurately and timely judge the potential motion damage. It also met the instability needs of the movement personnel of the acquisition system in the changing sports environment and provided a reliable guarantee for the safety and health of the sport personnel.

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