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feat: Adds a diffeormorphism for the harmonic oscillator #1004

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b7253e3
feat: Add diffeomorphism for harmonic oscillator
jstoobysmith Mar 25, 2026
9faa279
feat: modification
jstoobysmith Mar 26, 2026
9a54ef0
refactor: docs
jstoobysmith Mar 26, 2026
2ef8476
refactor: Lint
jstoobysmith Mar 26, 2026
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14 changes: 14 additions & 0 deletions PhysLean/ClassicalMechanics/HarmonicOscillator/ConfigurationSpace.lean
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Expand Up @@ -255,6 +255,20 @@ instance : CompleteSpace ConfigurationSpace := by
classical
simpa using (FiniteDimensional.complete ℝ ConfigurationSpace)

/-- The diffeomorphism between ℝ and ConfigurationSpace. -/
noncomputable def toRealDiffeo : Diffeomorph 𝓘(ℝ, ℝ) 𝓘(ℝ, ℝ) ℝ ConfigurationSpace ω where
toFun := fromRealCLM
invFun := toRealCLM
left_inv := by
intro t
cases t
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@zhikaip zhikaip Mar 25, 2026 •
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Suggested change
cases t

shouldn't need cases t here
(goes into CauSeq.Completion.Cauchy abs which is totally irrelevant here)

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@jstoobysmith jstoobysmith Mar 26, 2026

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Thanks - agreed. I also realised it is probably a bit stupid to add this and not simultaneously convert to EuclideanSpace. So will do that as well here.

rfl
right_inv := by
intro t
rfl
contMDiff_toFun := contMDiff_iff.mpr ⟨fromRealCLM.continuous, fun x y => contDiffOn_id⟩
contMDiff_invFun := contMDiff_iff.mpr ⟨toRealCLM.continuous, fun x y => contDiffOn_id⟩

/-!
## Map to space
-/
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