An isoperimetric problem for continuous systems: The aeolian vibration of a conductor span

The equations of motion for perfectly mechanical systems which are restricted to satisfy given constraints are derived through the Lagrangian formulation for continuous media. Hamilton's equations for this situation are derived, and the equations for the balance of energy and angular momentum are generated from fundamental principles. These equations are all specialized to the example of a conductor which is vibrating under Aeolian excitation. Various models for the Hamiltonian density and the constraint energy density due to the wind energy input are also discussed.