An Elementary Treatise on Quaternions |
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Page vii
... operators and functions : and therefore the student is not wholly unprepared to meet it . No one is puzzled by the fact that log.cos.x * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also ...
... operators and functions : and therefore the student is not wholly unprepared to meet it . No one is puzzled by the fact that log.cos.x * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also ...
Page viii
... operators and functions in other methods , that they are not generally commutative , is in Quaternions true in the multipli- cation of ( vector ) coordinates . It will be observed by those who are acquainted with the Cal- culus that I ...
... operators and functions in other methods , that they are not generally commutative , is in Quaternions true in the multipli- cation of ( vector ) coordinates . It will be observed by those who are acquainted with the Cal- culus that I ...
Page xiv
... operator which turns one vector into another . It is thus decomposable into two 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 ...
... operator which turns one vector into another . It is thus decomposable into two 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 ...
Page xix
... operator qs ( ) 9-8 turns the system it is applied to through 28 times the angle of q , about the axis of q . If the position of a system at time t is derived from the initial position by q ( ) 9 - 1 , the instantaneous axis is ...
... operator qs ( ) 9-8 turns the system it is applied to through 28 times the angle of q , about the axis of q . If the position of a system at time t is derived from the initial position by q ( ) 9 - 1 , the instantaneous axis is ...
Page 2
... 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 system , a point is defined by a single ...
... 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 system , a point is defined by a single ...
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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