COMPLIANT HYBRID MECHANICS · INDEPENDENT ROD TWIST · RISK-OPTIMAL CONTROL
M1 · ROLLING
TELEMETRY
———————————————
ADMISSIBILITY GUARDS
PHASE PORTRAIT · target capture corridor
RELEASE PREDICTOR · η(x) at current α
MISSION
—
0
00
TARGET
SEPARATION CONTROL
ROD ROTATION · ±5° nominal per rod
φc0.00°φΔ0.00°sΔ0.000
COMPLETE MECHANICS MODEL
Rigid-body foundation. Peng Xu, Richard E. Groff, and Timothy C. Burg derived and experimentally validated the nonlinear, underactuated, nonholonomic Shoot-the-Moon dynamics and model-based position control. This simulator treats that work as the rigid foundation.
Present extensions. Rolling loss, traction guards, elastic rail compliance and its fold, hybrid contact loss, scoring flight, timing risk, target viability, independent axial rotation of both rods, and compound opening–twist control.
Physical control correction. The real apparatus does not translate the complete rail assembly laterally. The simulator fixes the rail centerline: A/D rotate both rods together, while Q/E and U/O provide independent left/right twist.
η = d / 2(R+r), δ = √(1−η²), M = m(1+κ/δ²)ωₓ = −(r/R) φ̇cη ż = r φ̇Δvˣtw = r φ̇ᵢ (tᵢ × nᵢ) · eₓ
A fixed axial angle does not change a perfectly circular homogeneous rod; its rate changes contact-surface velocity. Static angle can matter through ovality, eccentricity, texture, wear, or anisotropic coating. The ±5° range is a nominal apparatus observation and should be measured on a physical unit.