##  [Principle of Least Action](/principle-least-action) 

  ##  [Principle of Least Action](https://natural.quantumdictionary.io/principle-least-action-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variational principle stating that the actual trajectory of a physical system between specified states makes the action — the time integral of the Lagrangian — stationary with respect to nearby variations of the path, typically yielding the equations of motion via the Euler–Lagrange equations.

 

 

 

 

 





 

 



 ##  [Principle of Least Action](https://mathlogic.quantumdictionary.io/principle-least-action-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variational principle stating that the true trajectory of a physical system between fixed endpoints makes the action functional stationary (typically an extremum), leading to the Euler–Lagrange equations that determine the system's evolution.

 

 

 

 

 





 

 



 ##  [Principle of Least Action](https://engineering.quantumdictionary.io/principle-least-action-2) 

  

 [![Engineering & Applied Technologies Dictionary](/sites/default/files/styles/large/public/2026-01/Engineering%20%26%20Applied%20Technologies.png.webp?itok=_IKO7_-n)](/topic-specific-dictionaries/engineering-applied-technologies)



**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variational principle stating that the actual trajectory of a mechanical system between two fixed states in time makes the action functional S = ∫_{t1}^{t2} L(q, q̇, t) dt stationary (δS = 0), where L is the system's Lagrangian (typically kinetic minus potential energy); the stationarity condition yields the Euler–Lagrange equations and thus the system's equations of motion in classical mechanic