An Elementary Treatise on Quaternions |
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Page xiv
... versors by arcs on the unit - sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) = Kr . Kq . § 55 . Proof of the Associative Law of Multiplication p.qr = pq.r. §§ 57-60 ...
... versors by arcs on the unit - sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) = Kr . Kq . § 55 . Proof of the Associative Law of Multiplication p.qr = pq.r. §§ 57-60 ...
Page xv
... 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 vectors at right angles to each other is a ...
... 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 vectors at right angles to each other is a ...
Page 26
... VERSOR , and is denoted by the letter U prefixed to the quaternion . 49. ] Thus , if OA = a , OB = ß , and if q be the quaternion which changes a to ẞ , we have B = qa , which we may write in the form B α = q , or βαι Ba - 1 = 9 , if we ...
... VERSOR , and is denoted by the letter U prefixed to the quaternion . 49. ] Thus , if OA = a , OB = ß , and if q be the quaternion which changes a to ẞ , we have B = qa , which we may write in the form B α = q , or βαι Ba - 1 = 9 , if we ...
Page 27
... versor of the quotient is quadrantal , i . e . it is a unit - vector . 50. ] We must now carefully notice that the quaternion which is the quotient when 8 is divided by a in no way depends upon the absolute lengths , or directions , of ...
... versor of the quotient is quadrantal , i . e . it is a unit - vector . 50. ] We must now carefully notice that the quaternion which is the quotient when 8 is divided by a in no way depends upon the absolute lengths , or directions , of ...
Page 28
... versor differs merely by the reversal of its representative angle . The versor , it must be remembered , gives the plane and angle of the turning - it has nothing to do with the extension . 52. ] The Conjugate of a quaternion q ...
... versor differs merely by the reversal of its representative angle . The versor , it must be remembered , gives the plane and angle of the turning - it has nothing to do with the extension . 52. ] The Conjugate of a quaternion q ...
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a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ