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The General Equations of Analytical Dynamics

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Modern Methods of Analytical Mechanics and their Applications

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 387))

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Abstract

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.

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Authors and Affiliations

  1. Russian Academy of Sciences, Moscow, Russia

    V. V. Rumyantsev

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  1. V. V. Rumyantsev
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  1. Russian Academy of Sciences, Russian

    Valentin V. Rumyantsev  & Alexander V. Karapetyan  & 

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© 1998 Springer-Verlag Wien

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Rumyantsev, V.V. (1998). The General Equations of Analytical Dynamics. In: Rumyantsev, V.V., Karapetyan, A.V. (eds) Modern Methods of Analytical Mechanics and their Applications. International Centre for Mechanical Sciences, vol 387. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2520-5_1

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  • DOI: https://doi.org/10.1007/978-3-7091-2520-5_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83138-0

  • Online ISBN: 978-3-7091-2520-5

  • eBook Packages: Springer Book Archive

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