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Energy integrals for the systems with nonholonomic constraints of arbitrary form and origin

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Abstract

This work analyzes energy relations between nonholonomic systems, whose motion is restricted by nonholonomic constraints of arbitrary form and origin. Such constraints can be natural, originating from spontaneous formulation of the problem, or artificial, expressing some program motion in control theory. On the basis of corresponding Lagrange’s equations, a general law of the change in energy dɛ/dt was formulated for such systems by the help of which it has been shown that here there exist two types of laws of conservation of energy, depending on the structure of work of these reaction forces. Also, the condition for existence of this second type of the law of conservation of energy has been formulated in the form of the system of differential equations. The results obtained are illustrated by a number of examples, with natural nonlinear constraints, as well as with artificial ones that express some program motion.

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Authors and Affiliations

  1. Faculty of Physics, University of Belgrade, Braće Jugovića 12, Belgrade, Serbia

    Djordje Mušicki

  2. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Belgrade, Serbia

    Djordje Mušicki

  3. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Belgrade, Serbia

    Dragomir Zeković

Authors
  1. Djordje Mušicki
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  2. Dragomir Zeković
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Correspondence to Dragomir Zeković.

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Mušicki, D., Zeković, D. Energy integrals for the systems with nonholonomic constraints of arbitrary form and origin. Acta Mech 227, 467–493 (2016). https://doi.org/10.1007/s00707-015-1403-6

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  • DOI: https://doi.org/10.1007/s00707-015-1403-6

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