Green's Theorem can be applied as a practical real-time algorithm to detect rotation from two orthogonal sensors by accumulating swept area. The core discrete integrator is S[n] = S[n-1] + (x[n]*(y[n]-y[n-1]) - y[n]*(x[n]-x[n-1]))/2, with a floating-point-friendly form and an integer/fixed-point-friendly form. The post analyzes noise behavior (approximating a Laplace distribution, growing as sqrt(N)), derives detection thresholds, discusses sampling rate tradeoffs, and demonstrates the algorithm with Python simulations. Key insight: signal grows linearly with samples while noise grows as square root, so detection is always achievable given enough time. Counterintuitively, sampling less often (with a minimum of 8-12 samples per cycle) can tolerate higher noise than oversampling without prefiltering.
