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

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• 作者：Hamad M. Yehia ^{hyehia@mans.edu.eg" class="auth_mail}
• 关键词：Rigid body dynamics ; Integrable cases ; Solvable cases ; Particular solutions ; Bobylev&ndash ; Steklov case
• 刊名：Mechanics Research Communications
• 出版年：April, 2014
• 年：2014
• 卷：57
• 期：Complete
• 页码：44-48
• 全文大小：376 K

文摘

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.