The Principles of Elliptic And Hyperbolic Analysis
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O\ sin w cos <^ Consequently we have for the elliptic axis OP, ^_ k{Gosv sinu- (^-{- cosi^sin^-y) — sinu sinv sin fSy a Vl — cosho PRINCIPLES OF ELLIPTIC AND HYPERBOLIC ANALYSIS. 13 The locus of the poles of the several elliptic areas is the original ellipsoid. To find the product of two ellipsoidal versors of the above general form. The two factor versors are expressed by n ^« = cos?^+ sinw(cos<^-A;y8— sin<^-«)^, and yf = cos v + sin v (cos cf>' -ky — sin <^' • «) ^ ; it is required to show that their product has the form rr ^" = cos 10 + sinw(cos(^"-A:e — sin(^"-a) ^. We have i"7f = (gosu + sin?/-^^) (cosv + sinv-r;^) = cosw cosv — sini^ sin v cos^ry n + \cosu sin -u- 77 + cos'U sinit-^ — sin it sin 1; Sin ^7; p. The problem is reduced to finding the value of cos ^7; and Sin ^7;. Now $rj means the elliptic versor between the elliptic axes cos (ft-k/^ — sin <^ • a and cos cf>' -ky — sin' • a.
To find them, we apply the following principle : Restore the elliptic axes to their spherical originals, find the versor between these unit axes according to the ordinary rule, and reduce its axes back to the ellipsoidal form.
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You can find similar books in the "Read Also" column, or choose other free books by Alexander Macfarlan to read online
To quickly assess the difficulty of the text, read a short excerpt:
O\ sin w cos <^ Consequently we have for the elliptic axis OP, ^_ k{Gosv sinu- (^-{- cosi^sin^-y) — sinu sinv sin fSy a Vl — cosho PRINCIPLES OF ELLIPTIC AND HYPERBOLIC ANALYSIS. 13 The locus of the poles of the several elliptic areas is the original ellipsoid. To find the product of two ellipsoidal versors of the above general form. The two factor versors are expressed by n ^« = cos?^+ sinw(cos<^-A;y8— sin<^-«)^, and yf = cos v + sin v (cos cf>' -ky — sin <^' • «) ^ ; it is required to show that their product has the form rr ^" = cos 10 + sinw(cos(^"-A:e — sin(^"-a) ^. We have i"7f = (gosu + sin?/-^^) (cosv + sinv-r;^) = cosw cosv — sini^ sin v cos^ry n + \cosu sin -u- 77 + cos'U sinit-^ — sin it sin 1; Sin ^7; p. The problem is reduced to finding the value of cos ^7; and Sin ^7;. Now $rj means the elliptic versor between the elliptic axes cos (ft-k/^ — sin <^ • a and cos cf>' -ky — sin
What to read after The Principles of Elliptic And Hyperbolic Analysis?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Macfarlan to read online
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