{"title":"陀螺的运动","authors":"J. Vrbik","doi":"10.3888/TMJ.14-4","DOIUrl":null,"url":null,"abstract":"A quaternion is a four-dimensional quantity consisting of a scalar, say A, and a threedimensional vector a, collectively denoted A a HA, aL. Addition of two quaternions is component-wise, (1) HA, aLÅ⊕ HB, bL = HA+ B, a+ bL, (we do not need to add quaternions in this article). Their multiplication follows the rule (2) HA, aLÄ⊗ HB, bL = HA Ba ÿ b , A b+ B aaäbL. It is important to note that such multiplication is associative (even though noncommutative). This can be verified by the following. 8A_, a_<Î8B_, b_< := 8A B a.b, A b + B a aäb< êê TrigReduce êê Simplify H8A, 8a1, a2, a3<<Î8B, 8b1, b2, b3<<LÎ8C, 8c1, c2, c3<< 8A, 8a1, a2, a3<<ÎH8B, 8b1, b2, b3<<Î8C, 8c1, c2, c3<<L êê Expand 80, 80, 0, 0<<","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Motion of a Spinning Top\",\"authors\":\"J. Vrbik\",\"doi\":\"10.3888/TMJ.14-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A quaternion is a four-dimensional quantity consisting of a scalar, say A, and a threedimensional vector a, collectively denoted A a HA, aL. Addition of two quaternions is component-wise, (1) HA, aLÅ⊕ HB, bL = HA+ B, a+ bL, (we do not need to add quaternions in this article). Their multiplication follows the rule (2) HA, aLÄ⊗ HB, bL = HA Ba ÿ b , A b+ B aaäbL. It is important to note that such multiplication is associative (even though noncommutative). This can be verified by the following. 8A_, a_<Î8B_, b_< := 8A B a.b, A b + B a aäb< êê TrigReduce êê Simplify H8A, 8a1, a2, a3<<Î8B, 8b1, b2, b3<<LÎ8C, 8c1, c2, c3<< 8A, 8a1, a2, a3<<ÎH8B, 8b1, b2, b3<<Î8C, 8c1, c2, c3<<L êê Expand 80, 80, 0, 0<<\",\"PeriodicalId\":91418,\"journal\":{\"name\":\"The Mathematica journal\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Mathematica journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3888/TMJ.14-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Mathematica journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3888/TMJ.14-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
四元数是由标量A和三维向量A组成的四维量，统称为AA HA, aL。两个四元数的相加是组件式的，(1)HA, aLÅ⊕HB, bL = HA+ B, A+ bL，(本文中我们不需要添加四元数)。它们的乘法符合(2)HA, aLÄ⊗HB, bL = HA Ba¾b, A b+ b aaäbL。重要的是要注意，这种乘法是结合的(即使是非交换的)。这可以通过以下方式进行验证。8现代,现代< I8B_, b_ < = 8 B a.b, B + B艺术展< ee TrigReduce ee简化H8A 8 a1, a2, a3 < < I8B 8 b1、b2、b3 < < LI8C 8 c1, c2, c3 < < 8 8 a1, a2, a3 < < IH8B 8 b1、b2、b3 < < I8C 8 c1, c2, c3 < < L ee扩大80、80、0、0 < <
A quaternion is a four-dimensional quantity consisting of a scalar, say A, and a threedimensional vector a, collectively denoted A a HA, aL. Addition of two quaternions is component-wise, (1) HA, aLÅ⊕ HB, bL = HA+ B, a+ bL, (we do not need to add quaternions in this article). Their multiplication follows the rule (2) HA, aLÄ⊗ HB, bL = HA Ba ÿ b , A b+ B aaäbL. It is important to note that such multiplication is associative (even though noncommutative). This can be verified by the following. 8A_, a_<Î8B_, b_< := 8A B a.b, A b + B a aäb< êê TrigReduce êê Simplify H8A, 8a1, a2, a3<<Î8B, 8b1, b2, b3<
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