Apex Helix — initial kinematic model

r(t) = ⟨x(t), y(t), z(t)⟩ · five C¹ segments · t treated as time · Part 2 refined energy model

Current segment

Lift hill

State at t

1 Lift 0–10 2 Crest & drop 10–14 3 Helix 14–14+2π 4 Climb 14+2π–18+2π 5 Brake run 18+2π–23+2π

t = 0.00 s

Speed

Drag to orbit · scroll to zoom · Space plays or pauses. Automatic playback advances the time parameter t along the piecewise centreline.