Variational principle

Japanese: 変分原理 - へんぶんげんり（英語表記）variational principle

A fundamental law of physics expressed in the form of the calculus of variations, which states that a physical quantity will have a minimum or maximum value with respect to a small change. Examples include Hamilton's principle and the principle of least action in mechanics, and Fermat's principle in optics. Physical laws are often expressed as differential equations, but when expressed as a calculus of variations, the physical meaning of the law is clear and it is guaranteed that the law does not depend on the coordinate system, and laws expressed as differential equations can also be derived from this.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

ある物理量が微小変化に関して極小値または極大値をとるという変分法の形式で物理学の基本法則を表わしたもの。その例には，力学ではハミルトンの原理，最小作用の原理，光学ではフェルマの原理などがある。物理法則は微分方程式で表わされることが多いが，変分式で表わすと，法則の物理的意味が簡明で，法則が座標系に依存しないことが保証され，また微分方程式で表わされる法則もこれから導き出される。

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