Strong degenerate constraining in Lagrangian dynamics

We study the strong constraining problem in Lagrangian dynamics in the degenerate codimension one case. This is the first time that degenerate potentials at the constraint are considered for this problem. These new results cover several real analytic potentials that the previous do not. Some counterintuitive effects of the degenerate constraining problem are discussed.

💡 Research Summary

The paper investigates the “strong constraining” problem for Lagrangian systems when the constraining potential is degenerate on a codimension‑one hypersurface. Classical results on strong constraining assume that the potential is non‑degenerate at the constraint (the Hessian is positive definite on the normal bundle). In contrast, the author allows the potential to vanish to higher order on the constraint, which leads to new phenomena in the limit of infinitely stiff potentials.

The setting is a smooth manifold (N) (dimension (\ge 2)) equipped with a kinetic energy (K_x(v)=\frac12|v|_x^2) induced by a Riemannian metric (\rho). The Lagrangian family is
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