一类变分问题在中学物理课外教学中的尝试

摘要

变分原理在物理学中具有相当的普遍性.本文尝试在中学物理教学中引入变分原理,通过使用变分原理将表面上不同的4个有趣的问题联系起来,展示这些问题应用变分原理的求解过程,分析其间的差异和联系,并考虑体系所受的约束条件,揭示体系内在的对称性.在教学过程中不仅考虑知识的传授,更考虑了学生认知的发展,循序渐进地将内容引向深入.%The variational principle is a quite universal principle in physics.This paper attempts to introduce the variational principle in physics teaching in middle school.Four interesting problems that appears quite different were connected through this principle.Their solution processes using the variational principle were presented and the difference and relation between them were analyzed.The constraint conditions on the relevant systems were also considered and the inherent symmetry of these systems were revealed.In the teaching process,we not only consider the teaching of knowledge,but also take into account the development of the students' cognition,thereby deepen our understanding step by step.