动能定理应用时的一个伪命题探讨

利用一个常见的动力学例子,证明了应用动能定理可能会得到错误的结论.首先,应用动能定理可以证明一根用弹簧连接的杆,当给其适当的初角速度后,杆可以从铅直位置转到水平位置;然后,利用动量矩定理及数值计算,指出用动能定理得到的结论是错误的;最后,研究了这根杆的复杂的动力学特性,用数值积分获得了它的相平面图,进一步指出了动能定理得到的结论是错误的.

Discussion on a wrong conclusion gotten by theorem of kinetic energy for a system

During solving a dynamic problem, it is argued that a wrong conclusion will be gained by theorem of kinetic energy for a system. Firstly, it is concluded that while gotten a proper initial angular velocity, a link connected to a spring can rotate from vertical position to horizontal position by theorem of kinetic energy for a system. Secondly, the conclusion proves to be wrong by moment of momentum theorem about an axis and numerical calculating. Finally, the link's complex kinetic characteristics are studied; and the conclusion by theorem of kinetic energy for a systems is proved to be wrong again.