https://affinedrift.com Affine control theory for golf swing dynamics - Research articles, models, and resources en-us contact@affinedrift.com contact@affinedrift.com Sun, 30 Aug 2026 20:23:36 GMT https://affinedrift.com/articles/zero-torque-counterfactual.html The Zero-Torque Counterfactual (ZTCF) family: definition, interpretation, and numerical computation algorithm for the AffineDrift golf swing framework. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/zero-torque-counterfactual.html https://affinedrift.com/articles/upstreamdrift-educational-integration.html Review of UpstreamDrift simulation platform capabilities and integration plan for the Geometry of Motion book series. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/upstreamdrift-educational-integration.html https://affinedrift.com/articles/theory-part5.html Simulink implementation documentation for the control-affine golf swing model, including numerical routines and validation approaches. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/theory-part5.html https://affinedrift.com/articles/theory-part4.html Modal approximations, wrench decomposition, and pendulum dynamics with detailed mathematical derivations for golf swing biomechanics. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/theory-part4.html https://affinedrift.com/articles/theory-part3.html Establishes drift invariance properties and develops a taxonomy of forces in the golf swing, analyzing the limitations of the affine control assumption. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/theory-part3.html https://affinedrift.com/articles/theory-part2.html Diagnostic tools for analyzing golf swing dynamics: the Zero Torque Counterfactual (ZTCF) family and Zero Velocity Counterfactual (ZVCF) for model-conditioned drift/input attribution. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/theory-part2.html https://affinedrift.com/articles/theory-part1.html Foundational derivation showing the golf swing as a control-affine mechanical system, introducing the drift/input decomposition framework for biomechanical analysis. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/theory-part1.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-7-residual-aware.html Using residuals as control and validation signals instead of ignoring them. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-7-residual-aware.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-6-hybrid.html How tangent-space reasoning changes across impacts, guards, and mode switches. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-6-hybrid.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-5-contraction.html Contraction certificates as tangent-space stability statements. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-5-contraction.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-4-residuals-curvature.html Residuals arise from curvature, not modeling error. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-4-residuals-curvature.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-3-control.html Control design in the tangent space. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-3-control.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-2-dynamics.html Infinitesimal dynamics and moving tangent spaces. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-2-dynamics.html https://affinedrift.com/articles/tangent-hyperplanes-series/part-1-geometry.html Geometric foundations for tangent hyperplanes. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplanes-series/part-1-geometry.html https://affinedrift.com/articles/tangent-hyperplane-articles/TABLE_OF_CONTENTS.html A guided route through exploratory notes on nonlinear control and geometric intuition. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/TABLE_OF_CONTENTS.html https://affinedrift.com/articles/tangent-hyperplane-articles/LAYMANS_TERMS_SUMMARY.html A non-technical overview of the tangent hyperplane framework and linear approximations in nonlinear control. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/LAYMANS_TERMS_SUMMARY.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Residual-Aware_Control_LAYMAN.html A non-technical explanation of residual-aware control and geometric curvature. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Residual-Aware_Control_LAYMAN.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Residual-Aware_Control_CRITIC.html Formal critique of Residual-Aware Control: Exploiting Geometric Curvature. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Residual-Aware_Control_CRITIC.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Hybrid_Tangent_LAYMAN.html A non-technical explanation of hybrid tangent spaces and non-smooth dynamics. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Hybrid_Tangent_LAYMAN.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Hybrid_Tangent_CRITIC.html Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Hybrid_Tangent_CRITIC.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Contraction_Tangent_LAYMAN.html A non-technical explanation of contraction theory and tangent spaces in control theory. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Contraction_Tangent_LAYMAN.html https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Contraction_Tangent_CRITIC.html Formal critique of Contraction Theory Meets Tangent Spaces — Unifying Stability and Optimality. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/tangent-hyperplane-articles/Advanced/Contraction_Tangent_CRITIC.html https://affinedrift.com/articles/rotation-representations-reference.html Comprehensive reference for conversion between rotation matrices, quaternions, Euler angles, and screw/axis-angle representations. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/rotation-representations-reference.html https://affinedrift.com/articles/rotation-converter.html Interactive calculator for converting between rotation matrices, quaternions, ZYX Euler angles, axis-angle, and exponential coordinates — with 3D screw axis visualization and step-by-step formulas. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/rotation-converter.html https://affinedrift.com/articles/proximal-distal-model-workbench.html Run the open double-pendulum, triple-pendulum, and bilateral golf models in matched PyQt6 and React/Tauri interfaces. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/proximal-distal-model-workbench.html https://affinedrift.com/articles/proximal-distal-falsification-atlas.html A governed map from prominent proximal–distal claims to alternative mechanisms, discriminating measurements, uncertainty, and exact falsifiers. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/proximal-distal-falsification-atlas.html https://affinedrift.com/articles/proximal-distal-energy-transfer.html An open, model-tiered analysis of distal handoff timing, interaction forces, segment work budgets, and falsifiable counterfactual tests. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/proximal-distal-energy-transfer.html https://affinedrift.com/articles/proximal-distal-a-journey-through-the-swing.html A full-length, accessible companion to the open proximal-to-distal energy-transfer study. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/proximal-distal-a-journey-through-the-swing.html https://affinedrift.com/articles/passive-distributed-control.html Integration of Frans Bosch's passive distributed control framework with the Geometry of Motion mathematical treatment. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/passive-distributed-control.html https://affinedrift.com/articles/ideomotor-theory-and-predictive-brain.html Cross-cutting treatment of ideomotor theory, predictive coding, and forward models as they relate to motor control and the Geometry of Motion framework. Sun, 30 Aug 2026 00:00:00 GMT https://affinedrift.com/articles/ideomotor-theory-and-predictive-brain.html