. The Bell System technical journal . a- CYLINDRICAL CO-ORDINATES IN STRAIGHT WAVEGUIDE. TOROIDAL CO-ORDINATES IN CURVED WAVEGUIDE Fig. 1 origin. If the wave guide is bent as shown on Fig. lb, but a wave frontat right angles to the cylinder axis is to be maintained, the waves must beshortened at the inside of the bend and lengthened at the outside of thebend. Regarding compression as a positive and expansion as a negativedeformation, one sees that the distortion of the wave shape is proportionalto the curvature of the wave guide multiplied by the cosine of the azimuthangle. It is natural to as
. The Bell System technical journal . a- CYLINDRICAL CO-ORDINATES IN STRAIGHT WAVEGUIDE. TOROIDAL CO-ORDINATES IN CURVED WAVEGUIDE Fig. 1 origin. If the wave guide is bent as shown on Fig. lb, but a wave frontat right angles to the cylinder axis is to be maintained, the waves must beshortened at the inside of the bend and lengthened at the outside of thebend. Regarding compression as a positive and expansion as a negativedeformation, one sees that the distortion of the wave shape is proportionalto the curvature of the wave guide multiplied by the cosine of the azimuthangle. It is natural to assume that the coupling between modes is propor-tional to this distortion. Now it is known that all modes of propagation in a circular wave guide CURVED WAVE GUIDES 3 can be derived from functions Jnix^) cos }up. In these functions, n iscalled the aximuthal index because it indicates the type of symmetry aroundthe circumference of the wave guide. When these characteristic functionsare multiplied by the distortion factor cosine (p, the resulting expressionsare proportional to the sum o
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
