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New integrable problems in rigid body dynamics with quartic integrals

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Abstract

We consider the general problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We will construct two new conditional integrable problems. These cases are combined generalizations of several previously known ones, namely those of Chaplygin and Yehia by the introduction of additional parameters to the structure of each.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, King Faisal University, P. O. Box 400, Al-Hassa, 31982, Saudi Arabia

    A. A. Elmandouh

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    A. A. Elmandouh

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  1. A. A. Elmandouh
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Elmandouh, A.A. New integrable problems in rigid body dynamics with quartic integrals. Acta Mech 226, 2461–2472 (2015). https://doi.org/10.1007/s00707-015-1320-8

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  • DOI: https://doi.org/10.1007/s00707-015-1320-8

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