import Mathlib.Data.Real.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2

noncomputable section

namespace QFD.Atomic.Chaos

/-- Minimal data for the spin–orbit vibration system. -/
structure VibratingSystem where
  r : EuclideanSpace ℝ (Fin 3)      -- Linear displacement
  p : EuclideanSpace ℝ (Fin 3)      -- Linear momentum
  S : EuclideanSpace ℝ (Fin 3)      -- Electron vortex spin
  k_spring : ℝ                      -- Shell theorem constant

/-- Pure Hooke contribution coming from the shell theorem. -/
def HookesForce (sys : VibratingSystem) : EuclideanSpace ℝ (Fin 3) :=
  -sys.k_spring • sys.r

end QFD.Atomic.Chaos