The General Equations of Analytical Dynamics

  • V. V. Rumyantsev
Part of the International Centre for Mechanical Sciences book series (CISM, volume 387)


Poincaré’s remarkable idea [1], [2] to represent motion’s equations of holonomic systems in terms of a certain transitive Lie group of infinitesimal transformations was extended by Chetayev [3]–[6] to the cases of rheonomic constraints and dependent variables, when transformation group is intransitive one. Chetayev transformed Poincaré’s equations to canonical form and elaborated the theory of their integration. These fine results were developed in a number of papers [7]–[23]. Our lectures represent an introduction in the theory of generalized Poincaré’s and Chetayev’s equations based on closed systems of transformations. These equations include both the motion’s equations in independent and dependent, holonomic and non-holonomic coordinates for holonomic and non-holonomic systems and in this sense are the general equations of analytical dynamics.


Rigid Body Analytical Dynamics General Equation Virtual Displacement Canonical Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • V. V. Rumyantsev
    • 1
  1. 1.Russian Academy of SciencesMoscowRussia

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