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.
Highlights
Works by Cortizo and Giacaglia [2], Kottke [8], and Giacaglia and Kottke [5] have described in details the formalism, which is the theoretical background of this work, by the introduction of virtual linear velocities and angular velocities and force-torque composed vectors representing kinematical and dynamical quantities of all links involved
In the present work we show a compact and straightforward method to obtain Euler-Lagrange’s Equations for such a mechanical system by writing down the Newton-Euler dynamical equations condensed into composed vectors and multiplying such equations by a properly chosen composed kinematical vector
The final differential equations are transformed by simple scalar products and it is shown that the resulting differential equations are completely equivalent to the differential equations obtained from the Lagrangian of the system
Summary
Works by Cortizo and Giacaglia [2], Kottke [8], and Giacaglia and Kottke [5] have described in details the formalism, which is the theoretical background of this work, by the introduction of virtual linear velocities and angular velocities and force-torque composed vectors representing kinematical and dynamical quantities of all links involved. In the present work we show a compact and straightforward method to obtain Euler-Lagrange’s Equations for such a mechanical system by writing down the Newton-Euler dynamical equations condensed into composed vectors and multiplying such equations by a properly chosen composed kinematical vector.
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