A Mathematical Model for Interaction Analysis Between Multiview Video System and User

2006 ◽  
pp. 375-384 ◽  
Author(s):  
You Yang ◽  
Gangyi Jiang ◽  
Mei Yu ◽  
Zhu Peng
Keyword(s):  
Mathematical Model ◽  
Interaction Analysis ◽  
Video System ◽  
Multiview Video

scholarly journals An approximate mathematical model for estimating the influence of vibrations on attached elements of a mobile robot video system

2021 ◽  
pp. 20-26
Author(s):  
A. A. Lobaty ◽  
M. М. Tatur ◽  
A. K. Ibrahim
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mobile Robot ◽  
Random Process ◽  
Random Vibration ◽  
Experimental Studies ◽  
Mobile Platform ◽  
Special Equipment ◽  
Video System ◽  
Vibration Process

The problem of constructing and applying of mathematical model for assessing the influence of vibrations on the attached elements of the video system of a mobile robot is solved. This robot is considered as a mobile platform for placing of the special equipment for various purposes. The analysis of mathematical models and the results of experimental studies of vibrations of multi-support wheeled machine and its structural elements has been conducted. On the basis of this analysis, the form of a stochastic mathematical model of vibrations of the structure of a mobile robot has been substantiated. The vibration model is specified as a correlation function or spectral density of a random process for various conditions of the robot’s movement. Differential equations of the shaping filter for modeling а random vibration process with given characteristics are presented. Differential equations for the probabilistic moments of the vibration process are presented. Based on the equations for the probabilistic moments and the proposed formula, an assessment of events, which consist in exceeding the vibration amplitude of a given level was carried out. These events are named as outliers of a random process and characterize the range within the basic properties of the equipment installed on the mobile platform are preserved. An analytical study of a mathematical model to determine the intensity of emissions of a random vibration process has been carried out. The probabilistic characteristics of the vibration process and the intensity of emissions are determined. The obtained theoretical results make it possible to assess the performance of the elements of a video system installed on a mobile platform and to formulate the basic requirements for tolerances for their parameters. The results of computer modeling clearly showed the efficiency of the proposed mathematical model for assessing the influence of vibrations.

Numerical simulation and characteristics investigation of golf ball trajectory

2019 ◽  
Vol 26 (3) ◽  
pp. 105-114
Author(s):  
Xi WANG ◽  
Hanyu CHEN ◽  
Xiaofeng LI
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Interaction Analysis ◽  
Peak Height ◽  
Combined Effects ◽  
Main Factors ◽  
Club Head ◽  
Ball Trajectory ◽  
The Mathematical Model ◽  
Launch Angle

In this study, MATrixLABoratory (MATLAB)’s ode 45 method was adopted to investigate the effects of the three main factors on golf trajectory characteristics, and the preferred striking conditions were concluded. Meanwhile, the results of interaction analysis were used to assess the dependence of carry distance and peak height on each factor. Eventually, the realistic normal swing tests were conducted in a laboratory to confirm the validation and accuracy of the mathematical model. The simulated results showed that a faster club head speed generally enabled to improve carry distance. However, once the rotational speed was more than 3,000 r·min-1, the increased tendency of carry distance turned to decrease. Moreover, the decreased tendency was aggravated as the increase of club head speed and launch angle, but the low launch angle benefited to alleviate the decrease. Compared to the carry distance, peak height always rose in any conditions. Meanwhile, the combined effects of the three factors on carry distance were more obvious than on the peak height. Finally, the optimised striking strategies were concluded for golfer-slow, golfer-medium and golfer-fast, respectively.

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