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alysoid |
exponentional |
with - π/2a < t < π/2a
The alysoid 1) is
a generalization of the catenary (a=1).
However, sometimes the alysoid is used as an alternative name for this catenary.
For a=2 the curve can be used to find an optimal acceleration profile.
The alysoid can be defined as the curve for which the center of curvature describes the path of a parabola,
when rolling over a straight line (with the parabola perpendicular to the straight
line).
It was Césaro who started to study the curves, in 1886.
The intrinsic Whewell equation of the alysoid has a rather simple form: s = tan aφ, s being the arc
length.
1) Alusion (Gr.) = little chain.