Reproducibility of Galley’s nonconservative Hamiltonian and equations of motion

Determine whether the nonconservative Hamiltonian and canonical equations presented in Galley (Phys. Rev. Lett. 110, 174301 (2013), Eqs. (12) and (17)) can be derived via a correct Legendre transform from the doubled-variable Lagrangian framework developed here, and, if so, provide the explicit derivation and assumptions under which they hold; otherwise, precisely identify the source of the discrepancy and the conditions under which Galley’s formulas fail.

Background

The paper develops a Hamiltonian formulation for nonconservative systems using a doubled-variable action, clarifying boundary conditions and constructing a corresponding family of gauge-related Hamiltonians via a Legendre transform. In doing so, the authors provide corrected expressions for the nonconservative Hamiltonian and Hamilton’s equations.

They explicitly note a discrepancy with the expressions reported in Galley (2013), stating that they cannot reproduce Galley’s nonconservative Hamiltonian and equations of motion (Eqs. (12) and (17) in that work). Resolving this discrepancy requires either a derivation that reconciles Galley’s formulas within the doubled-variable Legendre framework or a clear identification of why those formulas cannot be obtained under correct assumptions.