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quaternions    
四元法

四元法


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  • Quaternion - Wikipedia
    The scalar quaternions commute with all other quaternions, that is aq = qa for every quaternion q and every scalar quaternion a In algebraic terminology this is to say that the field of the scalar quaternions is the center of the quaternion algebra
  • Introducing The Quaternions - Department of Mathematics
    A useful mnemonic for multiplication is this picture: Figure: Multiplying quaternions Figure by John Baez If you have studied vectors, you may also recognize i, j and k as unit vectors The quaternion product is the same as the cross product of vectors: j = k; j k = i; k i = j: Except, for the cross product: i i = j j = k k = 0 while for quaternions, this is 1 In fact, we can think of a
  • Quaternion -- from Wolfram MathWorld
    The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton The idea for quaternions occurred to him while he was walking along the Royal Canal on his way to a meeting of the Irish Academy, and Hamilton was so pleased with his discovery that he scratched the fundamental formula of quaternion algebra, i^2=j^2=k^2=ijk=-1, (1) into the stone of the
  • What Is a Quaternion? The Math Behind 3D Rotation
    Quaternions are a type of math that handles 3D rotation more reliably than angles alone — here’s how they work and why they’re used in games and animation
  • Quaternions and spatial rotation - Wikipedia
    Quaternions and spatial rotation Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space (3D rotations) This is a generalization of the use of unit complex numbers for 2D rotations
  • 1. 2: Quaternions - Mathematics LibreTexts
    The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of 3-dimensional real space, extending the way that the complex numbers capture the …
  • Maths - Quaternions - Martin Baker - EuclideanSpace
    Quaternions have 4 dimensions (each quaternion consists of 4 scalar numbers), one real dimension and 3 imaginary dimensions Each of these imaginary dimensions has a unit value of the square root of -1, but they are different square roots of -1 all mutually perpendicular to each other, known as i,j and k
  • Lecture 5. Quaternions - Stony Brook University
    The set of unit quaternions is closed under quaternion multiplication, because the norm of the product of quaternions is the product of norms of the factors The inverse to a unit quaternion q 2 S3 coincides with q
  • 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 He devised them as a way of describing three-dimensional problems in mechanics
  • MATH431: Quaternions - UMD
    Thus unit quaternions correspond to rotations where the vector part corre-sponds to the axis of rotation and the angle is built into the scalar part and the magnitude of the vector part This is very important because when discussing rotations we can say that an arbitrary rotation can be performed via v 7!pvp where p is a unit quaternion





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