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Fig. 11-16. Derivation of

The correlation between an arc-length measurement and a rotation angle measurement can be derived from the infinitesimal spherical triangle shown in Fig. 11-16. and are the constant 9 and constant fi curves through A. By definition, 0i/4, is the angle between Lp and Let the attitude move an infinitesimal amount from A to A' along L9; then, fi will change by - Sfi perpendicular to Lg and 2 will change by 52, which gives an arc-length change of 52 sin/9 along Lp. From the infinitesimal right triangle ABA', we obtain tan6„

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