Analytical Approximate Solutions of a Magnetic Spherical Pendulum: Stability Analysis

Abstract Purpose Under certain conditions, the governing equation of motion magnetic spherical pendulum results in a cubic-quintic Duffing equation. The current work aims to achieve an analytical bounded procedure this Methods This may be accomplished by grouping nonlinear expanded frequency, Homotopy perturbation method (HPM), and Laplace transforms. Therefore, technique helps disregard appearance source secular terms. Results To validate obtained explanation, based on Runge–Kutta fourth order (RK4), numerical calculation is performed. On other hand, linearized stability analysis carried out explore neighbouring fixed points. Moreover, time history attained solution corresponding phase plane plots are expose influence affecting factors behavior motion. Conclusions A comparison between both solutions gives good matching them, which explores worthy accuracy approach question. Several portraits planned toward illustrating different types instability near equilibrium points, where relation cyclotron frequency (that generated field) characterized for diverse standards azimuthal angular velocity.