Hamilton's Principal Of Least Action

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Hamilton's Principal Of Least Action

The Action is defined as

\mathcal{J}=\int{\mathcal{L} dt}

Where

\mathcal{L}

is the Lagrangian of the mechanical system, and is defined by

\mathcal{L} = T - V

, where

T\

is the kinetic energy of the system, and

V\

is the potential energy.

When the all of the generalised coordinates of a system are known, the system obeys the Euler-Lagrange Equations ,

rac{d}{dt}\left(rac{\partial \mathcal{L}}{\partial \dot{q_i}}
ight) = rac{\partial \mathcal{L}}{\partial q_i},

for all

i=1,2,...,n.\

, where

q_1,q_2,...,q_n\

are the generalised coordinates of the system.

For a more detailed explanation of Lagragians, see the artical on the Lagrangian .

SEE ALSO

Action Principle

Hamiltonian Mechanics

Lagrangian Mechanics