A Simplified Force Equation for Coaxial Cylindrical Magnets and Thin Coils

A recently-published equation for calculating the force between coaxial cylindrical magnets is presented in simplified form. The revised equation is now very compact: it is defined with fewer parameters and contains fewer terms than the original equation. The new equation is purely real, unlike the original which contained imaginary components. As a result of the simplifications, the new equation is demonstrably faster to evaluate than the original, improving its utility for parametric optimization. A reference implementation is provided for Matlab and Mathematica.