Equations of motion of a multibody system and Lie groups


Type de document
Résumé / Abstract
Usually, the methods used for forming the equations relating to the motion of a complex system are based either on the use of general theorems or on the use of conventional techniques of analytical mechanics (Lagrange or Hamilton equations). In this case the formation of the equations of motion was made using a method allowing us to draft these equations in a more synthetic form. It uses the properties of the displacement group as a LIE group. Its main advantage is that it allows a totally intrinsic analytical calculation in the vector space of the wrenches or complex forces [8]. A symbolic calculus code has been designed in order to apply this approach. Initially, we have used and tested it in any open loop multibody system. The symbolic calculus code was applied, for instance, in the context of a study into the crash of a vehicle driven into a barrier. Key words: Lie groups;equations of motions;open-loop systems;multibody mechanics

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