Novel Approximations to the (Un)forced Pendulum–Cart System: Ansatz and KBM Methods

Abstract

In the present investigation, some novel analytical approximations to both unforced and forced pendulum–cart system oscillators are obtained. In our investigation, two accurate and effective approaches, namely, the ansatz method with equilibrium point and the Krylov–Bogoliubov–Mitropolsky (KBM) method, are implemented for analyzing pendulum–cart problems.The obtained results are compared with the Runge–Kutta (RK4) numerical approximation. The obtained approximations using both ansatz and KBM methods show good coincidence with RK4 numerical approximation. In addition, the global maximum error is estimated as compared to RK4 numerical approximation.