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quaternion    
n. 四个一组,四人一组,四元数

四个一组,四人一组,四元数

quaternion
四元数

quaternion
n 1: the cardinal number that is the sum of three and one [synonym:
{four}, {4}, {IV}, {tetrad}, {quatern}, {quaternion},
{quaternary}, {quaternity}, {quartet}, {quadruplet},
{foursome}, {Little Joe}]

Quaternion \Qua*ter"ni*on\, v. t.
To divide into quaternions, files, or companies. --Milton.
[1913 Webster]


Quaternion \Qua*ter"ni*on\, n. [L. quaternio, fr. quaterni four
each. See {Quaternary}.]
1. The number four. [Poetic]
[1913 Webster]

2. A set of four parts, things, or person; four things taken
collectively; a group of four words, phrases,
circumstances, facts, or the like.
[1913 Webster]

Delivered him to four quaternions of soldiers.
--Acts xii. 4.
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Ye elements, the eldest birth
Of Nature's womb, that in quaternion run. --Milton.
[1913 Webster]

The triads and quaternions with which he loaded his
sentences. -- Sir W.
Scott.
[1913 Webster]

3. A word of four syllables; a quadrisyllable.
[1913 Webster]

4. (Math.) The quotient of two vectors, or of two directed
right lines in space, considered as depending on four
geometrical elements, and as expressible by an algebraic
symbol of quadrinomial form.
[1913 Webster]

Note: The science or calculus of quaternions is a new
mathematical method, in which the conception of a
quaternion is unfolded and symbolically expressed, and
is applied to various classes of algebraical,
geometrical, and physical questions, so as to discover
theorems, and to arrive at the solution of problems.
--Sir W. R. Hamilton.
[1913 Webster]


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  • Quaternion - Wikipedia
    A quaternion that equals its real part (that is, its vector part is zero) is called a scalar quaternion (sometimes real quaternion or simply scalar), and is identified with the corresponding real number
  • 四元数（Quaternion）的概念和算法实现 - CSDN博客
    四元数（Quaternion）是表示物体在三维空间中旋转姿态的数学工具，相比欧拉角和旋转矩阵，它能避免万向节死锁、计算效率更高且插值更平滑，因此被广泛应用于机器人学、航空航天、游戏开发等领域。 _机器人四元数的含义
  • 四元数 (Quaternions) - 知乎
    推导过程参考： 四元数和旋转 (Quaternion rotation)，内容较为详细。 一旦构建好四元数，就不需要计算三角函数了。 因此实际上这个转换过程是高效的。 把一个正交矩阵 \mathbf {M}^q 转换为一个四元数 \hat {\mathbf {q}} 会稍微复杂一点。 关键点是下面从方程4 46中
  • Quaternion -- from Wolfram MathWorld
    While the quaternions are not commutative, they are associative, and they form a group known as the quaternion group By analogy with the complex numbers being representable as a sum of real and imaginary parts, , a quaternion can also be written as a linear combination
  • Lecture 5. Quaternions - Stony Brook University
    A quaternion of the form 0 + bi + cj + dk, where b; c; d 2 R is called pure imaginary If q = a + bi + cj + dk is any quaternion, then a is called its scalar part or real part and denoted by Re q and bi + cj + dk is called its vector part and denoted by Ve q
  • MATH431: Quaternions - UMD
    In H a rotation has an axis (of rotation) and each axis can be represented by a vector so it turns out that each unit pure quaternion corresponds to an axis of rotation
  • Quaternion | Rotations, Hypercomplex Numbers, Algebra | Britannica
    Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions Quaternions and rules for operations on them were invented by Irish mathematician Sir William Rowan Hamilton in 1843
  • What Is a Quaternion? The Math Behind 3D Rotation
    A quaternion is a number with four components: one real part and three imaginary parts Written out, it looks like q = w + xi + yj + zk, where w, x, y, and z are ordinary real numbers, and i, j, and k are three distinct “imaginary” units
  • Rotation Quaternions, and How to Use Them - DancesWithCode
    A quaternion with the value q = (1,0,0,0) is known as the identity quaternion, and will produce no rotation In this case, equation (5) will produce a rotation angle (θ) of zero, which is what we expect
  • Quaternion Algebras - Columbia University
    In Section 3, we then extend Hamilton’s quaternions to a more general framework of quaternion algebras And finally in Section 4, we extend quaternions even further into biquaternions to describe quaternion vectors with complex entries





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