Rotation of axes

Rotation of axes

Nonimaging Optical Systems

Published in Roland Winston, Lun Jiang, Vladimir Oliker, Nonimaging Optics, 2020

Roland Winston, Lun Jiang, Vladimir Oliker

By rotation of axes and translation of origin we can write down the equation of the meridian section of a CPC. In terms of the diameter 2a′ of the exit aperture and the acceptance angle θmax this equation is (rcosθmax+zsinθmax)2+2a′(1+sinθmax)2r−2a′cosθmax(2+sinθmax)2z−a′2(1+sinθmax)(3+sinθmax)=0

Functional-link Neural Networks and Visualization Means of Some Mathematical Methods

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Published in Hongxing Li, C.L. Philip Chen, Han-Pang Huang, Fuzzy Neural Intelligent Systems, 2018

Hongxing Li, C.L. Philip Chen, Han-Pang Huang

If we take a 45° rotation of axes and the new coordinates are denoted by x′1 and x′2, then the curve x1 + x2 = 2x1x2 = 1 can be expressed as follows: () −(x′2−22)2(22)2+(x′1)2(22)2=1

Light transmission performance of translucent concrete building envelope

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Published in Cogent Engineering, 2020

Baofeng Huang

The governing equations of the meridian section of a CPC are developed by rotation of axes and translation of origin. A compact parametric form can be presented by making use of the polar equation of the parabola. Figure 14 defined the key variables used in developing the meridian section as given by Equation (5) to Equation (8).

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Nonimaging Optical Systems

Functional-link Neural Networks and Visualization Means of Some Mathematical Methods

Light transmission performance of translucent concrete building envelope