Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy Multi-step Differential Transformation Method

In this letter, the equation of a particleʹs motion on a rotating parabolic surface is introduced through Lagrange equations and is solved by Multi-step Differential Transformation Method (Ms-DTM). As a main outcome, it is shown that this method gives approximations of a high degree of accuracy and least computational effort for studying particle motion on rotating parabolic surfaces compared to previous analytical methods. Also, position trajectory of the particle, r(t), and its phase planes are depicted in the current study for different constant numbers.