Accepted voltage balancing dynamics research methods flying capacitor converters are based on frequency domain transformations that involve double Fourier series with Bessel function coefficients. Therefore, these methods require high mathematical skills, are not truly analytical and difficult to use in engineering practice. In this paper, a "physical" approach to switched systems analysis based on stitching analytical solutions for consecutive switching subintervals, is applied to flying capacitor average voltage balancing dynamics analysis. It is shown that time domain averaging methodology generates simple analytical solutions that reveal the dependences on load parameters, carrier frequency, and normalized DC voltage command (AC modulation index). The power of suggested approach is demonstrated using single-leg converter voltage balancing dynamics analysis examples.