Citation:Sheehan, R. N. and Peters, F. H. (2016) 'Bends in the plane with variable curvature'. Bulletin of the Irish Mathematical Society, 78, pp. 61-80.
Abstract:
Explicit formulae for planar variable curvature bends are constructed using Euler’s method of natural equations. The bend paths are expressed in terms of special functions. It is shown that the length of the different bend types varies linearly with increasing radius and that the curvature of variable curvature bends can be expressed as a multiple of the curvature of a circle.
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