An Elementary Treatise on Quaternions |
From inside the book
Results 1-5 of 45
Page xiv
... Conjugate of a quaternion , and Kq = ( Tq ) 2q ~ 1 , qKq = Kq.q = ( Tq ) 2 . § 52 . Representation of versors by arcs on the unit - sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) ...
... Conjugate of a quaternion , and Kq = ( Tq ) 2q ~ 1 , qKq = Kq.q = ( Tq ) 2 . § 52 . Representation of versors by arcs on the unit - sphere . § 53 . Versor multiplication illustrated by the composition of arcs . § 54 . Proof that K ( gr ) ...
Page xvii
... conjugate , and πφ- Γλμ = Γ φ'λφ ' μ . Proof that m , whose value may be written as δ . φ ' λφ ' μόν δ.λμν , is the same for all values of λ , μ , v . §§ 144-146 . Proof that if where and mg = m + m1 g + m2 g2 + g3 , mi My § ( λφ ' μόν ...
... conjugate , and πφ- Γλμ = Γ φ'λφ ' μ . Proof that m , whose value may be written as δ . φ ' λφ ' μόν δ.λμν , is the same for all values of λ , μ , v . §§ 144-146 . Proof that if where and mg = m + m1 g + m2 g2 + g3 , mi My § ( λφ ' μόν ...
Page xviii
... conjugate , the roots of the cubic are real ; and the equation Урфр = 0 , or ( p - g ) P = 0 , is satisfied by a set of three real and mutually perpendicular vectors . Geometrical interpretation of these results . §§ 162-166 . Proof of ...
... conjugate , the roots of the cubic are real ; and the equation Урфр = 0 , or ( p - g ) P = 0 , is satisfied by a set of three real and mutually perpendicular vectors . Geometrical interpretation of these results . §§ 162-166 . Proof of ...
Page 16
... conjugate diameters . B t Again , p = at + or p = a tan x + ß cotx evidently represents a hyperbola referred to its asymptotes . But , so far as we have yet gone with the explanation of the calculus , as we are not prepared to determine ...
... conjugate diameters . B t Again , p = at + or p = a tan x + ß cotx evidently represents a hyperbola referred to its asymptotes . But , so far as we have yet gone with the explanation of the calculus , as we are not prepared to determine ...
Page 17
... conjugate diameters . If a , b , c be all positive , the surface is an ellipsoid . 32. ] In Example ( ƒ ) above we performed an operation equi- valent to the differentiation of a vector with reference to a single numerical variable of ...
... conjugate diameters . If a , b , c be all positive , the surface is an ellipsoid . 32. ] In Example ( ƒ ) above we performed an operation equi- valent to the differentiation of a vector with reference to a single numerical variable of ...
Other editions - View all
Common terms and phrases
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