The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página vi
... Tensors 22 ° . Definition of a scalar 23 ° . 93 29 unit - vector and a tensor 24 ° . Distinction between a scalar and a tensor PAGE 4 5 5 5 7 ∞ 00 CHAPTER II ON POINTS AND VECTORS IN A GIVEN PLANE SECTION 1 Linear Equations connecting ...
... Tensors 22 ° . Definition of a scalar 23 ° . 93 29 unit - vector and a tensor 24 ° . Distinction between a scalar and a tensor PAGE 4 5 5 5 7 ∞ 00 CHAPTER II ON POINTS AND VECTORS IN A GIVEN PLANE SECTION 1 Linear Equations connecting ...
Página ix
... Tensor and a Versor 15 ° . q = TqUq = UqTq 16 ° . U ( Uq ) = Uq • 43 44 SECTION 2 A Quaternion as the Sum of a Scalar and a Vector 17 ° . q = Sq + Vq • 18 ° . Recapitulation of the formulæ of 17 ° 19 ° . On the symbol , cos 0 + € sin 44 ...
... Tensor and a Versor 15 ° . q = TqUq = UqTq 16 ° . U ( Uq ) = Uq • 43 44 SECTION 2 A Quaternion as the Sum of a Scalar and a Vector 17 ° . q = Sq + Vq • 18 ° . Recapitulation of the formulæ of 17 ° 19 ° . On the symbol , cos 0 + € sin 44 ...
Página x
... IV EQUALITY AND INEQUALITY OF QUATERNIONS 40 ° . ( a ) Definition of equal quaternions . ( b ) On the equality of two tensors ( c ) 99 99 " " 29 99 versors 63 63 63 ART . 41 ° . If = a β δ ̓ X OUTLINES OF QUATERNIONS.
... IV EQUALITY AND INEQUALITY OF QUATERNIONS 40 ° . ( a ) Definition of equal quaternions . ( b ) On the equality of two tensors ( c ) 99 99 " " 29 99 versors 63 63 63 ART . 41 ° . If = a β δ ̓ X OUTLINES OF QUATERNIONS.
Página 8
... Tensor of B ( tendere , to stretch ) . Hence we have , В Tẞ = = ; Uß β = Τβυβ ; Uẞ = B ᎢᏰ ( 1 ) 24 ° . Since Tẞ is the ratio of two vectors with similar directions , ẞ and Uß , or -ẞ and -Uß , it is always posi- tive . Consequently ...
... Tensor of B ( tendere , to stretch ) . Hence we have , В Tẞ = = ; Uß β = Τβυβ ; Uẞ = B ᎢᏰ ( 1 ) 24 ° . Since Tẞ is the ratio of two vectors with similar directions , ẞ and Uß , or -ẞ and -Uß , it is always posi- tive . Consequently ...
Página 9
... tensor of a tensor is the tensor itself ; or , TT = T. If x and y be any scalars , S ( xp + y ) = y ; because хр is a vector , and a vector has no scalar part , just as a scalar has no vector part . The scalar of a scalar is the scalar ...
... tensor of a tensor is the tensor itself ; or , TT = T. If x and y be any scalars , S ( xp + y ) = y ; because хр is a vector , and a vector has no scalar part , just as a scalar has no vector part . The scalar of a scalar is the scalar ...
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Términos y frases comunes
arcs axis bisects centre chord circle coinitial vectors collinear commutative law conic conjugate consequently coplanar coplanar quaternions Crown 8vo diameter differential diplanar direction equal equation geometric given Hence hyperbola Illustrations intersection latus rectum Let OA locus mean point mẞ Multiplying OABC operation opposite P₁ parabola parallel parallelopiped perpendicular plane AOB positive or negative reciprocal right angles right quaternion right versors rotation Saß Saßy scalar Scientific Works published Similarly sphere SrVq ẞa symbols tangent TaTẞ tensor three vectors triangle Tẞ TẞTa unit-vector variable Vaß vector versor vertex VqVr VrVq Vẞy Woodcuts α α αβ β α βα φρ ОА ов ос тв وو ᎢᏰ
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