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Semi-analytical method used to determine intersections

Haerter, Jan O. ; Böing, Steven J. ; Henneberg, Olga ; Nissen, Silas Boye

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Título:
Semi-analytical method used to determine intersections
Autor: Haerter, Jan O. ; Böing, Steven J. ; Henneberg, Olga ; Nissen, Silas Boye
Assuntos: Atmospheric Dynamics ; Atmospheric Sciences ; Climate Change Processes ; Climate Science ; Cloud Physics ; Complex Physical Systems ; FOS: Earth and related environmental sciences ; FOS: Physical sciences ; Geometry ; Geophysics ; Meteorology ; Tropospheric and Stratospheric Physics
Descrição: (a) In general, three circles (shown in dark colors) defined by (x_i, y_i, R_i) where i ∈ {1, 2, 3} expand by the same distance dR (black lines) until they collide in the collision point (x_c, y_c). At that stage the three bigger circles (shown in light colors) are defined by (x_i, y_i, R_i + dR). (b) In order to analytically find the collision point, the entire system is translated and rotated in such a way that four parameters become zero. The smallest circle (dark red dot) is translated to origo and reduced to zero radius, while the second smallest circle (dark blue) is rotated onto the y-axis and reduced by the equivalent size. This translation makes the biggest circle (dark green) be defined by (x'_3, y'_3, R'_3), and the collision point is now at (x'_c, y'_c).
Editor: figshare
Data de criação/publicação: 2021
Idioma: Inglês

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