46 3 Symmetry of Second Rank Tensors, Cross Product
Hereeandu, withe·u=0, are orthogonal unit vectors. The parameterρis the
radius of the screw, projected into the in thee–u-plane. The sign of the chirality
parameter
χ=s( 2 π)·(e×u) (3.49)
determines, whether the curve describes a right-handed or a left-handed screw. The
magnitude ofχis the pitch of the screw. The chirality, being the spate product of
three polar vectors, is a pseudo vector, which changes sign under the parity operation.
3.5 Exercise: Velocity of a Particle Moving on a Screw Curve
Hint:Useα=ωtfor the parameter occurring in the screw curve (3.48),ωis a
frequency.