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Differential Geometry: Lecture 8: coframes and structure equations for R3
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We introduce the idea of a coframe. The attitude matrix is seen be shared by both the frame and coframe at once. Usual component expansions are derived. Finally we use the matrices of forms notation to efficiently derive the structure equations of Cartan. We then verify the results for the cylindrical and spherical frames. We also spend some time to sketch methods to derive the coframe in terms of differentials in the case the coframe corresponds to a coordinate system. No generality is attempted in that sketch and it probably can be improved.
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