On Euler-Lagrange's Equations: A New Approach

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


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.


composed vectors; connected rigid bodies; dynamics

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

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Trends in Computational and Applied Mathematics

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