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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:
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 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 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]].
[[Category:physics]]
[[Category:physics]]