Discrete Hamilton–Jacobi theory for systems with external forces

Abstract This paper is devoted to discrete mechanical systems subject external forces. We introduce a version of with Rayleigh-type forces, obtain the equations motion and characterize equivalence for these systems. Additionally, we Noether’s theorem other characterizing Lie subalgebra symmetries forced Lagrangian system. Moreover, develop Hamilton–Jacobi theory Hamiltonian These results are useful construction so-called variational integrators, which, as illustrate some examples, remarkably superior usual numerical integrators such Runge–Kutta method.