Applications of common energy variability methods for establishing the equilibrium equation in mechanics

Abstract The principles of the energy variation method are commonly utilized in mechanics. Energy is a scalar variable, so these more convenient and simple to establish equilibrium equations compared vector-based approaches (i.e. using forces displacements). present article applied theorem order set for various complicated problems. Four examples applying include differential equation Euler – Bernoulli beam based on method, system Equilibrium Equations Euler–Bernoulli with Least Work, principle maximum work motions motion by virtual theorem, have been implemented. results obtained from this study open up further research directions application mechanics as well analysis theory bridges.