On principles of stationarity for non-selfadjoint rod problems (Q1072759)

It is commonly assumed that nonconservative and, therefore, mathematically non-selfadjoint mechanical systems cannot be treated using variational principles. That is certainly true if one intended to apply, for example, Hamilton's principle or the principle of minimum potential energy. However, if one is ready to use other functionals than the energy or energy-like ones, and if one forgoes positive-definiteness allowing the functionals to be bilinear, one is able to derive principles of stationarity even in the case of non-selfadjoint systems. Rods subjected to uniformly distributed follower forces will be used as examples to demonstrate the existence of principles of stationarity.