Hamilton's principle for external viscous fluid-structure interaction

In this paper, Hamilton's principle is extended so as to be able to model external flow-structure interaction. This is accomplished by using Reynold's Transport theorem. In this form, Hamilton's principle is hybrid in the sense that it has an analytical part as well as a part that depends on experimentally derived functions. Examples are presented. A discussion on implications and extensions is extensive. In this work, the general theory is developed for the case where the configuration is not prescribed at the end times of the variational principle. This leads to a single governing equation of motion. This limitation can be removed by prescribing the end times, as is usual. This is outlined in the present paper, and will be the subject of a future paper.