螺旋理论的几何引论
A geometrical introduction to screw theory
摘要：
这项工作介绍了螺旋理论，一个古老的，但鲜为人知的理论，旨在描述刚体动力学。这种力学公式在螺旋的概念中统一了物体的平移和旋转自由度。它在机械动量和线速度之间，以及力和角速度之间找到了一个显著的数学类比。例如，它阐明了角速度应被视为施加的矢量，并且在运动的合成下，它们的总和与施加的力的规则相同。这项工作提供了一个简短而严格的介绍螺旋理论打算本科和一般读者。
英文摘要：
This work introduces screw theory, a venerable but yet little known theory aimed at describing rigid body dynamics. This formulation of mechanics unifies in the concept of screw the translational and rotational degrees of freedom of the body. It captures a remarkable mathematical analogy between mechanical momenta and linear velocities, and between forces and angular velocities. For instance, it clarifies that angular velocities should be treated as applied vectors and that, under the composition of motions, they sum with the same rules of applied forces. This work provides a short and rigorous introduction to screw theory intended to an undergraduate and general readership.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
