Improvement in the comprehensibility of the pioneering work of McIver

Hamilton’s principle is one of the most important milestones of analytical mechanics. This principle is valid for fixed mass and discrete material systems in its original form. The seminal work of McIver published in 1973 (McIver in J Eng Math 7(3):249–261, 1973) made this principle applicable to variable mass systems and has been constantly referenced due to the important results it revealed. However, the derivation of the expression in McIver’s paper may appear rather complex to some of the interested readers because some of the concepts and definitions used in the paper may be confusing for the reader. The main focus of this paper is to give this derivation in a more systematic and straightforward way through the Reynolds transport theorem without claiming any further scientific contribution. The discrepancies in the literature in terms of expressions and derivations were also discussed with the hope that it will help to remove some question marks in the minds of interested readers. This approach is later used to derive the coupled nonlinear equations of motion for moving mass on a flexible beam.