The Lagrangian and the second derivative?

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SUMMARY

The Lagrangian formulation of mechanics generally does not depend on higher derivatives of generalized coordinates, with exceptions noted in fields such as general relativity and elastomechanics. The discussion highlights that while higher derivatives can be relevant in specific contexts, such as quantum field theory (QFT), they often lead to inconsistencies. The lack of a comprehensive explanation for the general non-dependence on higher derivatives is acknowledged, emphasizing the need for further exploration in this area.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with generalized coordinates
  • Basic knowledge of general relativity
  • Introduction to quantum field theory (QFT)
NEXT STEPS
  • Explore the role of higher derivatives in general relativity
  • Investigate elastomechanics and its dependence on higher derivatives
  • Study the implications of higher derivatives in quantum field theory
  • Review classical mechanics principles related to the Lagrangian formulation
USEFUL FOR

Physicists, mechanical engineers, and students of advanced mechanics seeking to deepen their understanding of the Lagrangian formulation and its applications in various fields.

filip97
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Why Lagrangian not depend of higher derivatives of generalised coordinates ?
 
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Sometimes it depends, eg in general relativity or in elastomechanics. In most cases it does not, but there is no deeper explanation for that.

EDIT: AFAIK in QFT it would lead to inconsistencies, but I don't remember details.
 
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