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Two degree of freedom gyroscopic systems with linear integrals

Abstract

In this paper we consider the first integrals, linear in velocities, of conservative gyroscopic systems with two degrees of freedom. A precise criterion which specifies whether a given gyroscopic system possesses a linear integral is derived. When the kinetic energy has the structure of a standard form of the metric of revolution, all the possible systems which admit a linear integral and corresponding integrals are determined explicitly. Two examples are considered to illustrate the usefulness of the derived results.

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Acknowledgements

The work was partially supported by Montenegrin Academy of Sciences and Arts.

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Correspondence to Ranislav M. Bulatovic.

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Bulatovic, R.M., Kazic, M. Two degree of freedom gyroscopic systems with linear integrals. Meccanica 49, 973–979 (2014). https://doi.org/10.1007/s11012-013-9843-3

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  • DOI: https://doi.org/10.1007/s11012-013-9843-3

Keywords

  • Linear integral
  • Gyroscopic forces
  • Non-linear systems