Zdzisław Pluta, Tadeusz Hryniewicz, Novel Theory of Mathematical Pendulum Part 1, Volume 14, International Letters of Chemistry, Physics and Astronomy (Volume 14)
https://www.scipress.com/ILCPA.14.136
Abstract:
    In the paper, a new adequate theory of a simple mathematical pendulum is presented. This paper consists of two parts. In Part 1, the behaviour of pendulum in particular points, that is in central and terminal/extremum ones have been analyzed very carefully in detail. System of forces in these points was considered with a special attention turned towards the terminal points where the equilibrium of forces occurs and in the next moment the lack of that equilibrium takes place with the proof of the open polygon of forces as the condition of beginning of accelerated free variable motion. Part 2 of the paper is to be devoted to the kinetics of the pendulum weight presented by separating in it the descriptions of differentiated motion of this body in the consecutive neighbouring space-times corresponding with particular quarter-periods. In the conclusion, further elaborations in the subject are forecasted, regarding both dynamics and energy of the flat mathematical pendulum.
Keywords:
    Force Characteristics, Inertia, Mathematical Pendulum, Potential Field, Stable State, Unstable State