New Time-Integral Variational Principle

Time-integral variational principles offer a theoretical perspective and practical advantages. They provide a concept for understanding the behavior of dynamical systems and a means to develop governing equations of motion. In analytical mechanics, Hamilton’s principle is the most prominent variational principle and it is commonly connected to the classic Lagrange equations. This study extends those ideas by constructing time-integral variational principles from Nielsen’s form of Lagrange’s equations. The paper begins with a new development of Nielsen’s form, after which a set of new variational principles are developed and explained, followed by two example applications.