Rotation Equation of a Point in Air and its Solution

Tian-Quan Yun
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Tian-Quan Yun: School of Civil Engineering and Transportation, South China University of Technology, Wu Shan Lu 381, Tian He Qu, Guangzhou, 510641, P.R. China

Academic Journal of Applied Mathematical Sciences, 2022, vol. 8, issue 2, 30-33

Abstract: Operator ? inner products on both sides of Combination of Boyles’ law and Chares law (“B-C law†in short), we got the “Wind Speed Equation of a Point in Air†(“Wind Speed Equation†in short). It suits for describing straight-line motion, and It states that mu ? is in proportion to ?•T. Operator ? outer products on both sides of “Wind Speed Equation†(where T is replaced by T), we get the “Rotation Equation of a Point in Air†(“Rotation Equation†in short). It is a vector partial differential equation (PDE), suits for describing circular motion. It states that (mu ? ) is in proportion to T. Its solution is found by the method of separating variables. The existence of vector T is proved by the existence of rotation in the atmosphere and the solution of the “Rotation Equation†. It reveals that the vector form of B-C law holds in rotating air. Examples of up-side-down vertical rotation and horizontal rotation are given.

Keywords: Combination of Boyles’ law and Chares law; Newton’s second law; Rot (curl) operator; wind speed equation; operator; Inner product; Outer product; Method of separating variables. (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:arp:ajoams:2022:p:30-33

DOI: 10.32861/ajams.82.30.33

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