arXiv2026
Falling detection is vital for elderly care and intelligent surveillance; however, prevailing vision-based approaches predominantly frame it as static pose classification or discrete temporal pattern matching, fundamentally overlooking the instability dynamics of the human support system. This paper proposes a physics-informed falling detection framework that recasts falling as a stability-loss event in a coupled dynamical system. We introduce a novel dual-LTC architecture comprising a Center-of-Mass (CoM) subsystem and a Base-of-Support (BoS) subsystem, both instantiated as Liquid Time-Constant (LTC) neural networks to continuously model inertial trajectory evolution and ground-contact adjustment through adaptive time constants, Physical interpretability of falling motion. A learnable coupling module emulates physical interaction between the two subsystems, while a Stability Manifold classifier operates in the joint latent space to detect boundary crossing via Lyapunov-inspired stability metrics. Complementary counterfactual trajectory projection and Time-to-Collision (TTC) estimation further enable irreversibility assessment and early warning. The architecture is designed to support a three-state prediction paradigm (Normal, Falling, Fallen); in this preliminary study, we validate the core stability discrimination capability on a two-class dataset (Normal vs. Falling), leaving the full three-state temporal transition to future work. Unlike conventional CNN--RNN pipelines, the proposed formulation encodes continuous-time mechanical inertia, yielding a sub-50K-parameter network capable of real-time inference on resource-constrained edge devices. Extensive experiments demonstrate competitive accuracy with superior physical interpretability, validating its efficacy for low-compute visual fall detection.