Variational Method for Nonconservative Problems

Abstract

It is shown that the Ritz variational method can be applied to nonconservative problems provided the admissible velocity satisfies not only the geometric boundary condition but also a work condition on the part of the boundary surface where traction and traction rate are prescribed. It is further found that the modified variational principle can also be applied to nonconservative systems for which it is possible to construct an adjoint system. The principle is expected to be useful for application to a wide class of problems, including those encountered in connection with hydrodynamic and hydromagnetic stability investigation.