The study of the relative motion of a mechanism using Lagrange equations


  • Roxana Alexandra Petre Department of Mechanics of the University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania
  • Ion Stroe Department of Mechanics of the University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania


Lagrange equations, relative motion, inertial or noninertial reference frame


The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is studied. There are two cases studied: the first one when the first bar of the mechanism is hinged on a platform, which is considered initially to be fixed on the Earth’s surface, for the second case, the platform is in rotation with respect to Earth. For all the analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a program developed using the MATLAB software.


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