Semi-major and semi-minor axes

Mirrors

Published in Roshan L. Aggarwal, Kambiz Alavi, Introduction to Optical Components, 2018

where a and b are the semi-major and semi-minor axes of the ellipse. The focal lengths f1 and f2 of the ellipsoidal mirror are given by () f1=a−a2−b2 () f2=a+a2−b2

A Building-Specific Dynamic Loading Protocol for Experimental Tests on Nonstructural Elements

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Journal Information

Published in Journal of Earthquake Engineering, 2023

Yuteng Cao, Zhe Qu, Xiaodong Ji

Take the orbit in Fig. 16 for example. By the farthest point in the orbit from the origin, one can define a new coordinate system with a primary axis and a secondary axis. By finding a second point that is farthest to the primary axis, an ellipse can be uniquely defined. The semi-major and semi-minor axes of the ellipse are denoted as a and b, respectively. Furthermore, we denote the projection distance of the orbit on the major axis as and on the minor axis as . The flatness (F) and the eccentricity () of the orbit of any floor motion are then defined in Eq. (21) and Eq. (22), respectively. The flatness describes how an orbit is similar in amplitudes in two orthogonal directions, whereas the eccentricity describes how the orbit is symmetric around the original position.

Semi-major and semi-minor axes

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Mirrors

A Building-Specific Dynamic Loading Protocol for Experimental Tests on Nonstructural Elements