On Euler-Lagrange's Equations: A New Approach

G. E. O. Giacaglia, W. Q. Lamas

Abstract


A new formalism is proposed to study the dynamics of mechanical systems composed of N connected rigid bodies, by introducing the concept of $6N$-dimensional composed vectors. The approach is based on previous works by the authors where a complete formalism was developed by means of differential geometry, linear algebra, and dynamical systems usual concepts. This new formalism is a method for the description of mechanical systems as a whole and not as each separate part. Euler-Lagrange's Equations are easily obtained by means of this formalism.

Keywords


composed vectors; connected rigid bodies; dynamics

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References


S. F. Cortizo and G. E. O. Giacaglia, Dynamics of multibody: A geometric approach, 1993.

H. C. Kottke, Uma visão global de Newton-Euler aplicada à robótica, 2006.

G. E. O. Giacaglia and H. C. Kottke, The Newton-Euler Multibody Equations Revisited. Rio de Janeiro, RJ: Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM), 2007.

G. E. O. Giacaglia and W. Q. Lamas, Notes on Newton-Euler formulation of robotic manipulators, Proc. Inst. Mech Eng Pt K-J Multi-Body Dyn., vol. 226, pp. 61-71, 2012.

R. E. Roberson and R. Schawertassek, Dynamics of Multibody Systems. Berlin: Springer-Verlag, 1988.

J. Wittenburg, Dynamics of Systems of Rigid Bodies. Wiesbaden: Vieweg+Teubner Verlag, 1977.

A. A. Shabana, Dynamics of Multibody Systems. Cambridge: Cambridge University Press, 2013.

W. Schiehlen, Multibody Systems Handbook. Berlin: Springer-Verlag, 1990.

W. Schiehlen and P. Eberhard, Technische Dynamik. Wiesbaden: Springer-Verlag, 2017.

R. Featherstone, Rigid Body Dynamics Algorithms. Boston, MA: Springer US, 2008.

A. Goldenberg, B. Benhabib, and R. Fenton, A complete generalized solution to the inverse kinematics of robots, IEEE J. Robot. Autom., vol. 1, pp. 14-20, 1985.

G. E. O. Giacaglia, Mecânica Analítica. Rio de Janeiro, RJ: Almeida Neves, 1977.

J. E. Marsden and J. Scheurle, The reduced Euler-Lagrange equations, Fields Inst. Comm., vol. 1, pp. 139-164, 1993.

R. Abraham and J. E. Marsden, Foundations of Mechanics. Providence, RI: American Mathematical Society (AMS), 2008.

P. Libermann and C. M. Marle, Symplectic Geometry and Analytical Mechanics. Dordrecht: Springer Netherlands, 2012.




DOI: https://doi.org/10.5540/tema.2020.021.02.359

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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