A NEW RESEARCH-ORIENTED LECTURING METHODOLOGY OF CLASSICAL MECHANICS—VARIATIONAL PRINICPLES IN PARTICAL SYSTEMS AND ELASTIC CONTINUUM

This paper investigates theoretical connections between classical variational principles of discrete particle systems and variational principles of continuum/structures, from the perspective of research-oriented lecturing of classical mechanics. As continuum/structures could be regarded as particle systems with continuous spatial distributions, the classical variational principles in discrete particle systems are demonstrated to smoothly turn into the form of variational principles of continuum/structures, if the elastic interaction forces among particles being regarded as particular (conservative) active forces rather than internal constraint forces, and if the work done by these internal forces being correctly constructed. Through a detailed comparative study, the theoretical connections between two versions of variational principles, i.e., in discrete particle systems and in continuum/structures, respectively, will be explicitly demonstrated, and necessity of showing such connections in research-oriented lecturing of classical mechanics is also emphasized.