A new variational principle for dissipative systems with reverse time scales

Conventional Lagrangian functions L=L (t,q,q˙) are replaced by more general ones, L=L [t, q(t), q˙(t), q(t*), q˙(t*)], which depend on generalized coordinates q and velocities q˙ as functions of time measured along two reverse scales: t runs from 0 to T, while t*=T-t runs from T to 0. Generalized Lagrangian and Hamiltonian equations are derived, and applied to linear reciprocal systems with constant parameters. This formalism incorporates the dissipation effortlessly, which is the main reason for this development. The method obviates the need for an image (adjoint) system and attendant doubling of generalized coordinates, and leads to a new class of meaningful conservation laws