On Discrete Routh Reduction and Structures on the Reduced Space

The paper proves exactly the five ingredients the candidate outlines: (i) the reduced force is f̆_μ = −Ă_μ and −d f̆_μ = pr_2^*β_μ − pr_1^*β_μ with β_μ descending from d⟨μ,A⟩ (Proposition 3.23 and Corollary 3.24 in the paper ); (ii–iii) the magnetic modification on T*(Q/G_μ) yields a preserved two-form ω̆+ := (F+_{f̆μ}L̆_μ)^*(ω_{Q/G_μ} − π^*β_μ) for the reduced forced discrete flow (Proposition 2.25 and Theorem 2.28, then applied in Section 4; see , , ); (iv) identification with the unreduced regular system via Marsden–Weinstein reduction gives the equality of pullbacks and shows nondegeneracy (Proposition 4.1 and Proposition 4.5; see , ); and (v) from this, regularity of the reduced system follows (Theorem 4.6 ). The model’s derivation mirrors the paper’s structure and uses the same core identities, with only minor stylistic differences (e.g., directly recalling that ω_can − π^*β is symplectic on T*B).