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MENTAL MODEL · M5328

Hamilton's Principle

Hamilton's Principle
SystemsHigh supportSystems Theory
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

The evolution path of a dynamical system always makes the action (Action, the time integral of the Lagrangian) take an extremum (usually a minimum). It is the mathematical expression of nature's "least effort" principle.

SCAFFOLDING EFFECT

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Reduce cognitive load

The ultimate law of path optimization. Nature never wastes. If you find a process or habit very laborious (large action), it must be unstable and will eventually be replaced by a more "effort-saving" path. Optimization is finding the trajectory with the least action.

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Hamilton's principle (least action) states that the true motion makes the action integral stationary, providing a unified framework for analytical mechanics.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Hamilton%27s_principleZH · Explicit
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