A Lagrangian treatment of various forms of the rigid-body equations of motion is presented in this paper, including the most general expressions, which are the Boltzmann-Hamel equations. One key result that enables the derivations is the expression for the Hamel coefficients for the special case of rotational motion of a rigid body. The Hamel coefficients naturally arise in the Lagrange equations for quasi-coordinates. Another key result that enables the derivations is the expression for additional Hamel coefficients that arise when the translational-velocity vector of the mass center is coordinatized (expressed) along body-fixed axes. One interesting discovery is that the Boltzmann-Hamel equations are often misrepresented in standard textbooks. The misrepresentation stems from the fact that care is not exercised to distinguish the functional forms of the kinetic-energy expression.

中文翻译：

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刚体旋转运动的哈梅尔系数

本文介绍了各种形式的刚体运动方程的拉格朗日处理，包括最通用的表达式，即Boltzmann-Hamel方程。可以推导的一个关键结果是在特殊情况下刚体旋转运动的Hamel系数表达式。准坐标的拉格朗日方程自然会产生Hamel系数。能够进行推导的另一个关键结果是当沿身体固定轴协调（表示）质心的平移速度矢量时出现的其他Hamel系数。一个有趣的发现是，玻尔兹曼-哈默尔方程在标准教科书中经常被错误地表述。