Abstract
Formulation of analytical mechanics for viscous fluid is investigated in order to extend the limits of analytical mechanics to dissipative systems. A procedure to incorporate entropy with a Lagrangian function is performed based on the principle of local thermal equilibrium. Neumann's energy equation in irreversible thermodynamics is applied to derive viscous force from entropy. However, Neumann's energy equation itself is excluded from the Lagrangian function so that it should not explicitly violate time reversal invariance. Heat flow does not concern the equations of motion for fluid. This situation is explained by introducing a new vector field which is the time integral of entropy flow density divided by entropy density into the Lagrangian function. The existence of a new field quantity is regarded acceptable admitting the principle of local thermal equilibrium. The formulation of analytical mechanics for viscous fluid is thus successfully accomplished with the above-mentioned procedure. However, the existence of a new vector field is in the stage of mathematical conjecture. The strict proof of this is left for future study.
