Contributions to the mechanics of variable mass systems.

Author(s)

Leonardo Casetta

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2008-12-17

Examining board members

Celso Pupo Pesce; José Augusto Penteado Aranha; Ijar Milagre da Fonseca; Clodoaldo Grotta Ragazzo; Rubens Sampaio Filho

• Advisor: Celso Pupo Pesce

Abstract

Since 1814, when the first researches on the topic were carried out, variable mass system mechanics has become a particular branch within classical mechanics. Applied problems involving variable mass systems are sparsely distributed over a wide range of different areas of knowledge, and go from engineering to medicine, for example. However, despite these successful applications, even today one can find in the specialized literature discussions on the fundamentals of the variable mass system mechanics. In this scenario, apparent paradoxes, which are based on different equations of motion for a same variable mass system, figure out. In this sense, the Wagners problem, in the context of the study of the impact of solid bodies into liquid surfaces, and the falling chain problem can be cited as didactic examples. In this thesis, topics like this one will be treated. However, the main scope of this work is to present a more general and interpretative discussion on both the theory and application of the mechanics of variable mass systems, but keeping the focus on contributions that enable a better understanding of such an important branch of mechanics. For that, original theoretical results will be presented, as also discussions and applications of them. In the beginning, a discussion on the first fundamental works about the dynamics of a variable mass particle is done. In such a context, original interpretations of this author are pointed out. Then, the application of Lagrange equations on variable mass systems is discussed. In this scenario, this author shows the so-called Lagrange equation for a control volume where mass varies with generalized coordinates and velocities. This is also an original result of this thesis. By the end, an extension of a variational principle to a control volume is shown, also an original result of this work. Two classical problems within the theory of variable mass systems are then treated, i.e. the falling chain problem and the Wagners problems. Both are apparently paradoxical problems. The resolution of such apparent paradoxes is addressed, what is also an original result. Within the present context of the mechanics of variable mass systems, a brief discussion on the problem of the collapse of the World Trade Center twin towers is also done. (AU)