“least action, principle of”的概念、定义、翻译、参考文献-科学参考

least action, principle of

Mathematics

Consider a dynamical system with generalized coordinates q₁, q₂,…, q_n, solely acted on by conservative forces, with Lagrangian L. The action as the system moves from position at time t₁ to a position at time t₂ equals

$S = \int_{t_{1}}^{t_{2}} L (q, \dot{q}, t) d t .$

The principle of least action states that a trajectory of the dynamical system is an actual motion of the system if and only if the value of S is a stationary value. See also calculus of variations.

单词	least action, principle of
释义	least action, principle of Mathematics Consider a dynamical system with generalized coordinates q₁, q₂,…, q_n, solely acted on by conservative forces, with Lagrangian L. The action as the system moves from position at time t₁ to a position at time t₂ equals $S = \int_{t_{1}}^{t_{2}} L (q, \dot{q}, t) d t .$ The principle of least action states that a trajectory of the dynamical system is an actual motion of the system if and only if the value of S is a stationary value. See also calculus of variations.
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