On the Analytical Approximations to Kapitza’S Pendulum Oscillator Using Novel Techniques

This paper analyzes the Kapitza pendulum oscillator equation using analytical and numerical approaches. The equation is solved analytically using precise and practical methods, resulting in novel approximations. These approximations are then examined numerically through various examples. Moreover, a comprehensive comparison between the analytical and numerical approximations is examined. Also, the distance error is estimated compared to the Runge-Kutta numerical approximations. The techniques and approximations presented in this study have significant implications for modeling various physical and engineering problems, providing valuable insights for researchers in interpreting experimental results.