##  [Hamilton's Principle](/hamiltons-principle) 

  ##  [Hamilton's Principle](https://engineering.quantumdictionary.io/hamiltons-principle-0) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variational principle stating that the actual time evolution of a mechanical system between two fixed times makes the action integral S[q] = ∫_{t1}^{t2} L(q, q̇, t) dt stationary (extremal), where L is the Lagrangian (kinetic energy minus potential energy); the stationary condition yields the Euler–Lagrange equations which are the system's equations of motion under the chosen generalized coordin