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formal statement (Lean)
188noncomputable def harmonicFlow (m k : ℝ) (_hm : m > 0) (_hk : k > 0) : ℝ → PhasePoint → PhasePoint :=
proof body
Definition body.
189 fun t pt =>
190 let ω := Real.sqrt (k / m)
191 { q := pt.q * Real.cos (ω * t) + pt.p / (m * ω) * Real.sin (ω * t)
192 p := pt.p * Real.cos (ω * t) - m * ω * pt.q * Real.sin (ω * t) }
193
194/-- **THEOREM**: Energy is conserved along harmonic oscillator flow.
195
196 This is an explicit verification of energy conservation for the
197 harmonic oscillator, showing that Noether's theorem works. -/
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depends on (13)
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