On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations

Departing from d’Alembert’s principle, the classical deductions of Hamilton’s principle and, from it, of Lagrange's equations, are extended to the case of discrete systems of variable mass. These deductions recover the expressions of the extended Lagrange’s equations previously derived by Pesce [1] and of Hamilton’s principle proposed by Pesce and Casetta [19], for systems with mass explicitly dependent on position, velocity, and time. Alternative forms of Hamilton’s principle and Lagrange’s equations are obtained and presented. Cayleys’s falling chain problem is addressed as an application example.