The lagrangian dynamics in the context of the non-integer order calculus: fundamentals and applications

• Grant number: 10/15824-0
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2010
• End date: November 30, 2012
• Field of knowledge: Interdisciplinary Subjects
• Principal Investigator: Sergio Adriani David
• Grantee: Sergio Adriani David
• Host Institution: Faculdade de Zootecnia e Engenharia de Alimentos (FZEA). Universidade de São Paulo (USP). Pirassununga , SP, Brazil
• Associated researchers: clivaldo de oliveira

Abstract

The Lagrangian formalism in dynamical systems represents one of the most important principles in physics and is known to be enshrined. Meanwhile, in recent decades the non-integer order calculus or fractional calculus - so called more often - has become an important area of academic research and in industrial applications. Such applications of fractional calculus have been observed in several areas of knowledge and, among them, the Mechanics. Could be highlight applications in robotics, modal analysis, modeling and identification of thermal processes, control theory, among others. The main objective of this project is investigating the Euler-Lagrange equations for classical mechanical systems in the context of fractional calculus. The proposed study aims at analyzing the Euler-Lagrange formalism using the method of generalized derivatives of non-integer order . Moreover, it also intends to explore the formalism from that point of view, trying to apply it initially in various examples involving dynamic systems emphasizing a system mass-spring-damper described by non-integer order derivatives. The results may help to reveal the potential of the junction of these two tools, namely the Lagrange formalism in consolidated and emerging fractional calculation as an additional tool in solving problems involving mechanical systems. (AU)

Scientific publications

(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)

DAVID, S. A.; MACHADO, J. A. T.; QUINTINO, D. D.; BALTHAZAR, J. M.. Partial chaos suppression in a fractional order macroeconomic model. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 122, p. 55-68, APR 2016. (10/15824-0, 14/02041-9)

DAVID, S. A.; BALTHAZAR, J. M.; JULIO, B. H. S.; OLIVEIRA, C.; SIMOS, TE. Fractional Order and Dynamic Simulation of a System Involving an Elastic Wide Plate. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, v. 1389, p. 4-pg., 2011-01-01. (10/15824-0)

DAVID, S. A.; BALTHAZAR, J. M.; JULIO, B. H. S.; OLIVEIRA, C.; IOP. The fractional and nonlinear magneto-flexible rod. WAKE CONFERENCE 2021, v. 382, p. 6-pg., 2012-01-01. (10/15824-0)