New solvable problems in the dynamics of a rigid body about a fixed point in a potential field
Exactly Solvable and Integrable Systems
2013-03-26 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1303.5931,
title = {New solvable problems in the dynamics of a rigid body about a fixed point in a potential field},
author = {Hamad M. Yehia},
journal= {arXiv preprint arXiv:1303.5931},
year = {2013}
}