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

•Particle's motion on a rotating parabola surface has been introduced.•Lagrangian method is applied for governing equations.•Multi-step Differential Transformation Method is used for solving the problem.•Results have an excellent agreement with numerical fourth order Runge–Kutta method.•Particle position and phase plane were depicted.

In this letter, the equation of a particle's 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.

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