An Elementary Treatise on Quaternions |
From inside the book
Results 1-5 of 42
Page xiv
... factors , whose order is indifferent , the stretching factor or TENSOR , and the turning factor or VERSOR . These are denoted by Tq , and Uq . § 48 . The equation β gives α - B = qa q , or Ba1 , but not in general a 1ẞ = q . § 49 . q or ...
... factors , whose order is indifferent , the stretching factor or TENSOR , and the turning factor or VERSOR . These are denoted by Tq , and Uq . § 48 . The equation β gives α - B = qa q , or Ba1 , but not in general a 1ẞ = q . § 49 . q or ...
Page xv
... factor , may be considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two ...
... factor , may be considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two ...
Page 2
... factor √1 . Hence we may consider √1 as an operator , analogous to a handle perpendicular to the plane of xy , whose effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . - 5. ] In such a ...
... factor √1 . Hence we may consider √1 as an operator , analogous to a handle perpendicular to the plane of xy , whose effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . - 5. ] In such a ...
Page 26
... factor or agent which changes one definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 , is called the ...
... factor or agent which changes one definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 , is called the ...
Page 28
... factors is therefore merely to multiply twice over by the common tensor . 53. ] It is evident from the results of § 50 that , if a and ß be of equal length , their quaternion quotient becomes a versor ( the tensor being unity ) and may ...
... factors is therefore merely to multiply twice over by the common tensor . 53. ] It is evident from the results of § 50 that , if a and ß be of equal length , their quaternion quotient becomes a versor ( the tensor being unity ) and may ...
Other editions - View all
Common terms and phrases
a₁ axes axis Cartesian centre Chapter circle condition cone conjugate cöordinates coplanar curvature curve cylinder developable surface direction drawn easily Eliminating ellipsoid equal equation becomes evidently expression extremity Find the equation Find the locus formula given equation given lines given point gives Hamilton Hence integral intersection LAOB last section length linear and vector normal obviously once operating origin osculating plane parallel perpendicular properties prove quaternion radius rectangular system represents result right angles rotation S.aßp S.aßy Sapa Saß scalar scalar equations second order shew sin sin sin solution sphere spherical conic Spopp ẞ² suppose surface of revolution tangent plane tensor tetrahedron theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor write written Τρ φρ