中文摘要：

讨论动力学普遍定理对弹性细杆的表现形式。基于平面截面假定，以微段杆为对象，导出动量定理、动量矩定理和动能定理对弹性细杆的表达式；为明确三者的相互关系，分别从弹性细杆动量方程和动量矩方程以及离散系统的动能定理导出弹性细杆能量方程。因存在时间和弧坐标两个自变量，除关于时间的能量定理外，还存在关于弧坐标的能量定理，显示了弹性杆的特殊性。研究结果表明，对于不受分布力和约束的情形，三者具有相同的数学形式，即等式一边为对弧坐标的全偏导数，另一边是对时间的全偏导数。为进一步研究弹性细杆的守恒运动及其守恒量奠定了基础。

英文摘要：

General theorems of dynamics for the thin elastic rod are discussed. Taking a rod with different length as an object and based on Plane Section Assumption, mathematical formulas of theorem of momentum, theorem of movement of momentum and theorem of kinetic energy for the thin elastic rod are derived from those discrete mechanical systems. The theorems of kinetic energy of the rod are also obtained from the theorem of momentum and Theorem of movement of momentum of the rod. In addition to the existing theorems of kinetic energy of the rod about the time, there exists one about arc coordi- nate of the rod, which explains the particularity of the elastic rod dynamics. The results show that they have the same mathematical form and one side of the equation is a total patial derivative of a quantity with respect to the time and the other is a total patial derivative of another quantity with respect to the arc coordinate, when there are no distributing forces acting on the rod. The paper will provide basis of studying conservative motion and conservative quantity of the rod for next step.