{"title":"空气中一点的旋转方程及其解","authors":"Tian-quan Yun","doi":"10.32861/ajams.82.30.33","DOIUrl":null,"url":null,"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.","PeriodicalId":375032,"journal":{"name":"Academic Journal of Applied Mathematical Sciences","volume":"67 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Rotation Equation of a Point in Air and its Solution\",\"authors\":\"Tian-quan Yun\",\"doi\":\"10.32861/ajams.82.30.33\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":375032,\"journal\":{\"name\":\"Academic Journal of Applied Mathematical Sciences\",\"volume\":\"67 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Academic Journal of Applied Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32861/ajams.82.30.33\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Academic Journal of Applied Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32861/ajams.82.30.33","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Rotation Equation of a Point in Air and its Solution
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.