An Etymological Dictionary of Astronomy and Astrophysics

Of all the possible paths along which a → dynamical system can move from one configuration to another within a specified time interval (consistent with any constraints), the actual path followed is that which minimizes the time integral of the → Lagrangian function. Hamilton’s principle is often mathematically expressed as δ∫Ldt = 0, where L is the Lagrangian function, the integral summed from t₁ to t₂, and δ denotes the virtual operator of Lagrangian dynamics and the → calculus of variations.

See also: → Hamiltonian function;
→ principle.