We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a
generalized formulation of Lagrangian mechanics that can incorporate degenerate
Lagrangians as well as holonomic and nonholonomic constraints. We refer to the
generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For non-
degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to
the recently developed nonholonomic Hamilton–Jacobi theory. We are particularly …