Difference between revisions of "Principle of Least Action"

From Conservapedia
Jump to navigation Jump to search
m (Reverted edits by Conservativeamerican (Talk) to last revision by Aschlafly)
Line 1: Line 1:
 
The '''Principle of Least Action''' is an assumption of efficient motion in physics whereby a particle of fixed overall potential and kinetic energy follows the path that minimizes its action.
 
The '''Principle of Least Action''' is an assumption of efficient motion in physics whereby a particle of fixed overall potential and kinetic energy follows the path that minimizes its action.
−
 
−
Its actions is defined as:
 
−
 
−
<math>S=\int_{t_i}^{t_f}Ldt</math>
 
−
 
−
where <math>L=L(x,x',t)</math> is the [[Lagrangian]] of the system. The path that minimizes the action is the path that satisfies the [[Euler-Lagrange equation]]:
 
−
 
−
:<math>\frac{\partial L}{\partial x_i}= -\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial x'_i}</math>
 
−
 
−
for all i=1,2...N.
 
  
 
Variations on this principle include the insights that:
 
Variations on this principle include the insights that:
Line 18: Line 8:
 
This principle is a physical extension of the Euclidean theorem that the shortest distance between two points is a straight line.
 
This principle is a physical extension of the Euclidean theorem that the shortest distance between two points is a straight line.
  
−
The doctoral thesis of American physicist [[Richard Feynmann]] applied the Principle of Least Action to [[quantum mechanics]], and later built on that work to generate "Feynman diagrams," for which he won a shared [[Nobel Prize]].
+
The doctoral thesis of physicist [[Richard Feynmann]] applied the Principle of Least Action to [[quantum mechanics]], and later built on that work to generate "Feynman diagrams," for which he won a shared [[Nobel Prize]].
 
[[Category:physics]]
 
[[Category:physics]]

Revision as of 16:28, May 28, 2010

The Principle of Least Action is an assumption of efficient motion in physics whereby a particle of fixed overall potential and kinetic energy follows the path that minimizes its action.

Variations on this principle include the insights that:

  • a multi-body system will come to rest at a position that minimizes overall potential energy.
  • light takes the shortest path to travel between two points

This principle is a physical extension of the Euclidean theorem that the shortest distance between two points is a straight line.

The doctoral thesis of physicist Richard Feynmann applied the Principle of Least Action to quantum mechanics, and later built on that work to generate "Feynman diagrams," for which he won a shared Nobel Prize.

Retrieved from "https://www.conservapedia.com/index.php?title=Principle_of_Least_Action&oldid=782610"