Elements of Quaternions

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Ginn, Heath, & Company, 1887 - 234 σελίδες

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Περιεχόμενα

Coinitial vectors
13
Examples
14
Expression for a medial vector
15
Expression for an anglebisector
16
Examples
17
Analytical expression for a quaternion Product and quo tient of rectangular unitvectors Tensor and versor of
24
Symbolic notation q TqUq
25
Reciprocal of a quaternion
26
Quadrantal versors i j
27
Mean point
28
Whole powers of unit vectors Square of a unit vector is
29
Negative sign commutative with i j
30
Commutative law not true for the products of i j
31
CHAPTER II
32
A unit vector commutative with its reciprocal Reciprocal
33
Product and quotient of any two rectangular vectors
34
Equal quaternions 23 Positive rotation
35
00 00 +10 3 3
36
Exercises
37
Symbolic notation qSq +
38
4
39
Products of two vectors Symbolic notation
40
General principles and formulae
41
Powers of vectors and quaternions
42
Relation between the vector and Cartesian determination of a point
43
Right complanar diplanar and collinear quaternions Any two quaternions reducible to the forms
44
Reciprocal of a vector scalar and quaternion
45
Conjugate of a vector scalar and quaternion
46
Opposite quaternions
47
5
48
Representation of versors by spherical arcs
49
Addition and subtraction of quaternions K S and V dis tributive symbols K commutative with S and V T and U not distributive symbols
50
Multiplication of quaternions not commutative UnqпUq TпqпTq Kqr KrKq Product or quotient of com planar quaternions
51
Distributive and associative laws in quaternion and vector
52
General formulae
53
Applications
54
Formulae relating to the products of two or more vectors
55
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Σελίδα 193 - The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the major axis as diameter. 3. The locus of the point of intersection of perpendicular tangents is a circle with radius Va>

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