Transactions on Machine Design Slavko Rupcic, Vanja Mandri-Radivojevic and Nataša Nešic 11 2 2023 https://doi.org/10.6025/tmd/2023/11/2/33-42 https://www.dline.info/tmd/fulltext/v11n2/tmdv11n2_1.pdf In this work, we applied Vilenkin’s additional theorem among the circular apertures to measure the coupling calculations. We measure the vector-Legendre transformations of basis and test functions by keeping the domain over the aperture at an arbitrary level. With the help of Euler’s formula for rotating the coordinate system, we used the classical approach for the numerical measurements, which is more time intensive. With Vilekin’s additional theorem for Legendre functions, we increased the rotation-based measurements.