On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

Management of Port Solid Waste Framework

One of contemporary environmental issues refers to progressive and diverse generation of solid waste in urban areas or specific, and requires solutions because the traditional methods of treatment and disposal are becoming unviable over the years and, consequently, a significant contingent of these wastes presents final destination inappropriate. The diversity of solid waste generated as a result of human activities must have the appropriate allocation to specific legislation in force, such as landfill, incineration, among other procedures established by the competent bodies. Thus, also the waste generated in port activities or proceeding vessels require classification and segregation for proper disposal later. This article aims at presenting a methodology for the collection, transportation, treatment and disposal of solid waste port and also application of automation technology that makes possible the implementation of the same.