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.

Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange's equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

Synthesis and Solar Cell Application of New Alternating Donor-Acceptor Copolymers Based on Variable Units of Fluorene, Thiophene, and Phenylene

A new series of donor acceptor copolymers were synthesized via the Witting route and applied as an active layer in organic thin-films solar cells. These copolymers are composed of fluorene thiophene and phenylene thiophene units. The ratio between those was systematically varied, and copolymers containing 0%, 50%, and 75% of phenylene thiophene were characterized and evaluated when used in photovoltaic devices. The copolymers' composition, photophysical, electrical, and morphological properties are addressed and correlated with device performance. The 50% copolymer ratio was found to be the best copolymer of the series, yielding a power conversion efficiency (PCE) under air mass (AM) 1.5 conditions of 2.4% in the bilayer heterojunction with the C-60 molecule. Aiming at flexible electronics applications, solutions based on the heterojunction of this copolymer with PCBM (6,6-phenyl-C-61-butyric acid methyl ester) were also successfully deposited using an inkjet printing method and used as an active layer in solar cells.