This paper systematically explains and studies the intermediate axis instability phenomenon observed in the free rotation of a rigid body with three different principal moments of inertia

which is known in the academic community as the "tennis racket theorem" or "Janibekov effect". The paper avoids complex mathematical derivation symbols and instead adopts a method combining physical image description and qualitative analysis to deeply explore the underlying mechanism of this classical mechanical phenomenon. The research first constructs a geometric model of the phase space for the rigid body's rotation without external torque. Through the topological intersection lines of the energy ellipsoid and the angular momentum ellipsoid

it intuitively reveals the evolution trajectory of the angular velocity vector in three-dimensional space and the saddle point characteristics of the separation line. Based on this

the paper elaborates on the essential nature of stability when rotating around the maximum and minimum principal axes

as well as the intrinsic instability root of the disturbance growing exponentially when rotating around the intermediate principal axis. For the nonlinear evolution stage under large disturbances

this paper introduces the physical meaning of Jacobi elliptic functions

describes the process of periodic redistribution of angular velocity components among the three principal axes

and divides the flipping motion into three typical stages: quasi-stable rotation

rapid flipping

and quasi-periodic reciprocation. Further

the paper deeply explores the regulatory laws of key dynamic parameters such as the initial angular velocity

initial offset angle

and the ratio of moments of inertia on the flipping behavior

and clarifies the deterministic correlation between each parameter and the flipping period. Finally

combined with the experimental verification results of precision 3D-printed specimens

this study analyzes the high consistency between theoretical predictions and measured data and the sources of errors. This research aims to provide clear and intuitive physical cognition and theoretical support for fields such as spacecraft attitude control

sports biomechanics

and micro-nano robot design.