The Dzhanibekov Effect Revisited: Informational Hysteresis, Anisotropic Latency Fields, and Regime Transitions in Torque-Free Rotation

The Dzhanibekov effect—also known as the tennis racket theorem in its classical formulation—remains one of the most visually striking and widely circulated demonstrations of rotational instability in torque-free motion. A rigid body spinning about its intermediate principal axis undergoes abrupt, repeated flips that appear paradoxical to non-specialists and counterintuitive even to many trained physicists when encountered as a real-world phenomenon rather than as a textbook theorem. Conventional mechanics accounts for this behavior through the instability of the intermediate axis in Euler’s equations; however, this explanation is typically framed as a binary statement (“stable” versus “unstable”) and rarely develops a deeper dynamical interpretation of three experimentally salient features: (i) the emergence of highly organized, quasi-periodic flips rather than unstructured chaos; (ii) the strong dependence of the observed flip dynamics on preparation, perturbations, and real-world imperfections; and (iii) the apparent “memory” of the system, which repeatedly returns to similar macroscopic configurations despite inevitable dissipation and microstructural coupling.In this paper, we propose a rigorous reinterpretation of the Dzhanibekov effect within the framework of Viscous Time Theory (VTT), viewing the flip not merely as a consequence of intermediate-axis instability, but as a coherence-regime transition in an anisotropic informational geometry. We introduce an informational manifold for rigid-body rotation, in which rotational states evolve along constrained trajectories shaped by anisotropic reconfiguration costs associated with the principal inertia structure and by an effective informational viscosity arising from internal mode coupling and finite-time redistribution. In this picture, the flip is not an instantaneous kinematic accident but a finite-time transition between metastable corridors of rotational coherence, with the observed quasi-periodicity emerging as a geometric consequence of navigation along preferred informational pathways.This formulation yields a set of quantitative, testable predictions absent from the standard narrative, including hysteresis under cyclic control of initial conditions, direction-dependent flip thresholds and transition times, metastable latency regimes, and scaling relations linking flip timing to an informational viscosity parameter. To assess these predictions, we perform a comprehensive numerical validation combining high-resolution integration of the Euler equations, ensemble statistics over large sets of perturbations, spectral and structural diagnostics, multi-precision convergence testing, and comparative model analysis.Quantitative analysis demonstrates that informational viscosity produces a bounded suppression of instability growth (approximately 2–15%) without altering phase-space topology, integrability, or scaling structure. No chaotic attractors, bifurcation cascades, or nonphysical divergences emerge. The Dzhanibekov instability remains fundamentally geometric, with VTT operating as a coherent rate-level regulator rather than a replacement mechanism. This bounded rate modification becomes logarithmically amplified in flip-time statistics, providing a clear and measurable experimental signature.By reframing one of the most iconic “video-paradox” phenomena of classical mechanics as an informational hysteresis and regime-transition process, this work provides a mathematically grounded bridge between visible macroscopic dynamics and a general theory of anisotropic, viscous informational evolution. The Dzhanibekov effect thus emerges not only as a pedagogical curiosity, but as a quantitative macroscopic laboratory for probing informational geometry, coherence regimes, and finite-time reconfiguration in real physical systems.