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The main purpose of this study is to explore the feasibility of achieving a fourth integral for a charged rigid body (RGB) rotary movement, considering the influence of gyrostatic torque (GT) and a uniform electromagnetic field. Six nonlinear first-order differential equations (DEs) and their three first integrals, pertaining to geometry, area, and energy, regulate this problem. The analytical solution to the issue necessitates approaching a crucial fourth integral. This paper presents a pivotal criterion for a function F , contingent on all RGB variables, to qualify such integral is outlined. The achieved outcomes are validated through comparing them with the renowned cases and then they can be considered a consolidation or mainstreaming of prior research efforts.
Amer et al. (Thu,) studied this question.