Determinant of helical resistance in resistive-force theory ($AD-B^2={\ell }^2{a}^2{\xi }_{\parallel }{\xi }_{\perp }$)

Local resistive-force theory for a helix gives $AD-B^2={\ell }^2{a}^2{\xi }_{\parallel }{\xi }_{\perp }$. Positive local drag therefore guarantees a positive-definite axial resistance matrix and positive viscous power loss. The identity also keeps the denominator in counterrotating two-helix balances positive.