A new integrable problem with a quartic integral in the dynamics of a rigid body
Abstract
We consider the problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce a new integrable case, valid on zero level of the cyclic integral, that generalizes the known case of motion of a body in liquid due to Chaplygin and its subsequent generalization by Yehia. Apart from certain singular potential terms, the new case involves finite potential and gyroscopic forces, which admit physical interpretation as resulting from the interaction of mass, magnetized parts and electric charges on the body with gravitational, electric and magnetic fields.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- April 2013
- DOI:
- 10.1088/1751-8113/46/14/142001
- arXiv:
- arXiv:1302.7057
- Bibcode:
- 2013JPhA...46n2001Y
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- This work will appear shortly in "Journal of Physics A: Mathematical and Theoretical"