Five Mathematical Structural Models in Natural Philosophy with Technical Physical Quaternions |
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Page 88
... axiator The comparison of ax with the general instantaneous was in ( 5.1 ) connected with the octa- Cayley rotation ... axiator and components M we write exactly as in ( 2.4 ) ( 2.5 ) ( 2.6 ) etc with the only 8888 IV Comparison with the ...
... axiator The comparison of ax with the general instantaneous was in ( 5.1 ) connected with the octa- Cayley rotation ... axiator and components M we write exactly as in ( 2.4 ) ( 2.5 ) ( 2.6 ) etc with the only 8888 IV Comparison with the ...
Page 89
... axiator . The similarity of its structural features with those of the corresponding octavector axiators Kof ( 5.1 ) , III ( 3.14 ) and the corresponding relativistic velo- city axiator : K ++ W = W kw - i kv ++ 22 of III ( 5.8 ) ( 5.9 ) ...
... axiator . The similarity of its structural features with those of the corresponding octavector axiators Kof ( 5.1 ) , III ( 3.14 ) and the corresponding relativistic velo- city axiator : K ++ W = W kw - i kv ++ 22 of III ( 5.8 ) ( 5.9 ) ...
Page 90
... axiator ( 6.3 ) . Compari- son between both leads to : H ~ b -D ~ E -ε ~ d B ~ d ( 6.8 ) which in the case of ... axi- ator ( 6.5 ) discloses , perhaps , the most intimate electrome- chanical analogies by its connexions on the one hand ...
... axiator ( 6.3 ) . Compari- son between both leads to : H ~ b -D ~ E -ε ~ d B ~ d ( 6.8 ) which in the case of ... axi- ator ( 6.5 ) discloses , perhaps , the most intimate electrome- chanical analogies by its connexions on the one hand ...
Contents
ON QUATERNIONS 1 Introduction | 1 |
Extension to fourspace conceptions 3 Technical physical quaternions | 3 |
Affinors 1347 | 4 |
Copyright | |
97 other sections not shown
Common terms and phrases
3-waves according affinor axiator basic vectors bracket Broglie wave calculate Cayley Cayley transformation coefficients completed pyramid complex components connected connexion conservation theorem corresponding counterpart covariant curl current quaternion curvilined coordinate deformation density detailed Dirac equations direction displacement dyadic products elastic electric electromagnetic field electromagnetic potential electron elements energy energy-momentum tensor expression four-space geometry Hamilton's hexavector homogeneous Hund imaginary indicated invariant Lanczos linear Lorentz transformation magnetic matrix matter field Maxwell equations Maxwell's medium function motion equations motor multiplication norm obtained octavector orthogonal particle potential pyramid probability current quadric quantum mechanics quaternionian potential radius vector represents rotational hexavector scalar Schrödinger equation second model six-space substituted Synge technical physical quaternions theorem theory three-space tion translarotation v.Mises vanishes velocity wave equation wave fronts wave function yields