Spiral Hall

Spiral length design

On the circular curve, lateral acceleration affects comfort. On the spiral, both lateral acceleration and jerk affect comfort.  The determination of maximum curving speed on the basis of lateral acceleration only is not critical because the lateral acceleration is proportional to the square of speed whereas jerk is proportional to cubic power of speed. The maximum speed on a curve is thus signi...

اثر هال (hall effect)

Spiral spline interpolation to a planar spiral

We derive regions for T-cubic and arc/T-cubic spirals to two-point Hermite interpolation in terms of unit tangent vectors with help of Mathematica. The use of spirals gives the designer an excellent and speedy control over the shape of curve that is produced because there are no internal curvature maxima, curvature minima, inflection points, loops and cusps in a spiral segment.

TITLE Spiral

Spiral is a program generation system (software that generates other software) for linear transforms and an increasing list of other mathematical functions. The goal of Spiral is to automate the development and porting of performance libraries. Linear transforms include the discrete Fourier transform (DFT), discrete cosine transforms, convolution, and the discrete wavelet transform. The input t...

Spiral Knots

Spiral knots are a generalization of torus knots we define by a certain periodic closed braid representation. For spiral knots with prime power period, we calculate their genus, bound their crossing number, and bound their m-alternating excess.