ADVANCED STUDIES ON THE MECHANICS OF VARIABLE MASS SYSTEMS

• Grant number: 12/10848-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2012
• End date: August 31, 2016
• Field of knowledge: Engineering - Mechanical Engineering
• Principal Investigator: Celso Pupo Pesce
• Grantee: Leonardo Casetta
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 13/02997-2 - Lagrangian and Hamiltonian formalism for non-material volumes, BE.EP.PD

Abstract

Variable mass systems mechanics is the branch of Mechanics within systems which show variation in the amount of mass to them associated are considered. There is an inherent issue in the treatment of this kind of system. Principles of Mechanics were originally conceived for constant mass systems. Thus, the prime form of the representative equations of such principles cannot be straightly applied on variable mass systems. Technical literature shows that the construction of a mathematical formalism that is suitable to the treatment of this particular class of system has not been an easy process. Although such investigations have begun in the early twenties, misconceptions with respect to the application of mechanical fundamentals within the context can still be found. Moreover, new theoretical investigations are required. Modern science reveals a series of practical problems whose solution essentially depends on the concepts of variable mass systems mechanics. Interesting examples are rocket propulsion, tethered satellites, rotor dynamics in textile industry and vertical collapse of buildings. However, enough motivation can even be found in the many unsolved theoretical difficulties. The proposed research aims to consider some issues within the scenario, i.e. the construction of a consistent mathematical formalism that shows to be suitable to the treatment of variable mass systems. In this sense, particular problems which are relevant to the area experts will be considered.

Scientific publications

(9)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CASETTA, LEONARDO. A theorem on energy integrals for linear second-order ordinary differential equations with variable coefficients. Applied Mathematics Letters, v. 51, p. 8-12, JAN 2016. (12/10848-4)

CASETTA, LEONARDO; PESCE, CELSO P.. The inverse problem of Lagrangian mechanics for Meshchersky's equation. ACTA MECHANICA, v. 225, n. 6, p. 1607-1623, JUN 2014. (12/10848-4, 13/02997-2)

CASETTA, LEONARDO. Theorem on a new conservation law for the dynamics of a position-dependent mass particle. ACTA MECHANICA, v. 228, n. 1, p. 351-355, JAN 2017. (12/10848-4)

CASETTA, LEONARDO. Note on a Noetherian conservation law and its corresponding general class of nonlinear second-order ordinary differential equations. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, v. 97, n. 2, p. 240-246, FEB 2017. (12/10848-4)

CASETTA, LEONARDO. The inverse problem of Lagrangian mechanics for a non-material volume. ACTA MECHANICA, v. 226, n. 1, p. 1-15, JAN 2015. (12/10848-4, 13/02997-2)

CASETTA, LEONARDO; IRSCHIK, HANS; PESCE, CELSO PUPO. A generalization of Noether's theorem for a non-material volume. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, v. 96, n. 6, p. 696-706, JUN 2016. (12/10848-4, 13/02997-2)

CASETTA, LEONARDO. Geometric theory on the dynamics of a position-dependent mass particle. ACTA MECHANICA, v. 227, n. 6, p. 1519-1532, JUN 2016. (12/10848-4)

CASETTA, LEONARDO; PESCE, CELSO P.. A brief note on the analytical solution of Meshchersky's equation within the inverse problem of Lagrangian mechanics. ACTA MECHANICA, v. 226, n. 7, p. 2435-2439, JUL 2015. (12/10848-4)

CASETTA, LEONARDO; PESCE, CELSO P.. The generalized Hamilton's principle for a non-material volume. ACTA MECHANICA, v. 224, n. 4, p. 919-924, APR 2013. (12/10848-4)