arXiv subjects

Hamad M. Yehia

Publications and source records attributed to Hamad M. Yehia.

3 recordsLinked to original sources

arXiv2013

New solvable problems in the dynamics of a rigid body about a fixed point in a potential field

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed.

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arXiv2013

A new integrable problem with a quartic integral in the dynamics of a rigid body

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 interaction of mass, magnetized parts and electric charges on the body with gravitational, electric and magnetic fields.

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arXiv2012

A new 2D integrable system with a quartic second invariant

In the present note we introduce a new solution of this equation, lead- ing to a new integrable system with a quartic integral, which involves 16 free parameters. A special case of the new system admits interpretation in a problem of rigid body dynamics. It gives a new integrable variation of the cases due to Kovalevskaya (1889), Chaplygin (1903) Goriatchev (1916) and Yehia (2006).

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