Motion of a Spinning Top

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<

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陀螺的运动

四元数是由标量A和三维向量A组成的四维量，统称为AA 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 < <

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