Transition Curves Defined in the Polar Coordinate System

2017 ◽  
pp. 59-61
Author(s):  
Andrzej Kobryń
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Transition Curves

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

scholarly journals Aerosol Plume Detection Algorithm Based on Image Segmentation of Scanning Atmospheric Lidar Data

2016 ◽  
Vol 33 (4) ◽  
pp. 697-712 ◽  
Author(s):  
R. Andrew Weekley ◽  
R. Kent Goodrich ◽  
Larry B. Cornman
Keyword(s):  
Coordinate System ◽  
Original Data ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Lidar Data ◽  
Image Processing Algorithm ◽  
Polar Coordinate ◽  
Scanning Lidar ◽  
Performance Statistics ◽  
Background Fields

AbstractAn image-processing algorithm has been developed to identify aerosol plumes in scanning lidar backscatter data. The images in this case consist of lidar data in a polar coordinate system. Each full lidar scan is taken as a fixed image in time, and sequences of such scans are considered functions of time. The data are analyzed in both the original backscatter polar coordinate system and a lagged coordinate system. The lagged coordinate system is a scatterplot of two datasets, such as subregions taken from the same lidar scan (spatial delay), or two sequential scans in time (time delay). The lagged coordinate system processing allows for finding and classifying clusters of data. The classification step is important in determining which clusters are valid aerosol plumes and which are from artifacts such as noise, hard targets, or background fields. These cluster classification techniques have skill since both local and global properties are used. Furthermore, more information is available since both the original data and the lag data are used. Performance statistics are presented for a limited set of data processed by the algorithm, where results from the algorithm were compared to subjective truth data identified by a human.

Vehicle Kinematic State Estimation Using Passive Sensor Fusion Approach

2012 ◽  
Vol 271-272 ◽  
pp. 1709-1712 ◽  
Author(s):  
Li Wei Fong ◽  
Pi Ching Lou ◽  
Ke Jia Tang
Keyword(s):  
Coordinate System ◽  
Autonomous Navigation ◽  
Weighted Least Squares ◽  
Hierarchical Architecture ◽  
Estimation Accuracy ◽  
Polar Coordinate System ◽  
Global Estimate ◽  
Polar Coordinate ◽  
Passive Sensor ◽  
Cartesian Coordinate

The main issue addressed here is that of estimating the kinematic state components of a vehicle in autonomous navigation using landmark angle-only measurements from an onboard passive sensor. The estimates of the absolute position and velocity of the vehicle are provided by a hybrid coordinate fusion filter. The hierarchical architecture of the filter which consists of a group of local processors and a global processor is developed for improving estimation accuracy. In each local processor, an extended Kalman filter uses hybrid information from the reference Cartesian coordinate system and the modified polar coordinate system for state and state error covariance extrapolation and updating. In the global processor, a weighted least squares estimator is utilized to combine the outputs of local processors to form a global estimate. By using only two landmarks simulation results show that proposed algorithm improves the estimation accuracy drastically.

Polar Coordinate System

2016 ◽  
Author(s):  
H. M. Kingston ◽  
M. L. Kingston
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Polar Coordinate
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