论文标题
非惯性扭矩和Euler方程
Non-inertial torques and the Euler equation
论文作者
论文摘要
描述刚体旋转动力学的基本方程是$ {\vecτ} = d {\ vec l} / dt $，这是牛顿第二种运动定律的直接结果，仅在惯性坐标系统中有效。尽管为实际目的，该方程是由惯性观察者写下来的，但它是在通常固定在刚体中的非惯性辅助坐标系中进行的。这导致了著名的Euler方程，用于刚体的旋转。我们表明，只要考虑了非惯用扭矩，也可以从非惯性观察者的角度描述刚体的旋转动力学（用固定在刚体中的辅助坐标系旋转）。我们明确计算非惯性扭矩，并根据刚体的物理特征表达它们。我们表明，所得的动态方程精确地恢复了Euler方程。
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec τ}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system. While this equation is written down by an inertial observer, for practical purposes, it is worked out within a non-inertial ancillary coordinate system which is typically fixed in the rigid body. This results in the famous Euler equation for rotation of the rigid bodies. We show that it is also possible to describe the rotational dynamics of a rigid body from the point of view of a non-inertial observer (rotating with the ancillary coordinate system fixed in the rigid body), provided that the non-inertial torques are taken into account. We explicitly calculate the non-inertial torques and express them in terms of physical characteristics of the rigid body. We show that the resulting dynamical equations exactly recover the Euler equation.
