Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.15498 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910223434776576 |
|---|---|
| author | Shi, Peng |
| author_facet | Shi, Peng |
| contents | From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently, expressing the differential form of energy conservation in an arbitrary coordinate system and performing suitable differential operations yields Lagrange's equations. Generalized forces and generalized displacements are shown to be component representations of forces and displacements in a chosen coordinate system. Consequently, the essence of Lagrange's equations is identified as the transformation of the kinetic energy theorem into the momentum theorem via the chain rule for composite functions, thereby revealing how energy conservation constructs momentum conservation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Essence of Lagrange's Equations Shi, Peng Classical Physics From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently, expressing the differential form of energy conservation in an arbitrary coordinate system and performing suitable differential operations yields Lagrange's equations. Generalized forces and generalized displacements are shown to be component representations of forces and displacements in a chosen coordinate system. Consequently, the essence of Lagrange's equations is identified as the transformation of the kinetic energy theorem into the momentum theorem via the chain rule for composite functions, thereby revealing how energy conservation constructs momentum conservation. |
| title | On the Essence of Lagrange's Equations |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2605.15498 |