On Euler-Lagrange’s Equations: A New Approach

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

Authorship

G. E. O. GIACAGLIA ^**Corresponding author: G. E. O. Giacaglia - E-mail: giacaglia@gmail.com

Post-graduate Programme in Mechanical Engineering, Department of Mechanical Engineering, University of Taubaté, Rua Daniel Danelli, s/n, 12060-440, Taubaté, SP, Brazil. - E-mail: giacaglia@gmail.comUniversity of TaubatéBrazilTaubaté, SP, BrazilPost-graduate Programme in Mechanical Engineering, Department of Mechanical Engineering, University of Taubaté, Rua Daniel Danelli, s/n, 12060-440, Taubaté, SP, Brazil. - E-mail: giacaglia@gmail.com

http://orcid.org/0000-0002-1030-4863

W. Q. LAMAS

Lorena School of Engineering, University of São Paulo, Estrada Municipal do Campinho, s/n, 12602-810, Lorena, SP, Brazil. - E-mail: lamaswq@gmail.comUniversity of São PauloBrazilLorena, SP, BrazilLorena School of Engineering, University of São Paulo, Estrada Municipal do Campinho, s/n, 12602-810, Lorena, SP, Brazil. - E-mail: lamaswq@gmail.com

http://orcid.org/0000-0002-7588-0335

*Corresponding author: G. E. O. Giacaglia - E-mail: giacaglia@gmail.com

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