Discussion Overview
The discussion centers around the search for literature that applies Lagrangian or action principles in the context of continuum mechanics, specifically fluid mechanics and elasticity. Participants explore the availability of comprehensive resources similar to Landau's works in mechanics and electromagnetism, while addressing the challenges and limitations of deriving certain fluid dynamics equations from action principles.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant inquires about books that comprehensively use action principles in fluid mechanics and elasticity, similar to Landau's approach.
- Another participant suggests A. Sommerfeld's "Lectures on Theoretical Physics" as a potential resource, noting its value despite being in German.
- A later reply mentions that it seems proven that Navier-Stokes equations cannot be derived from an action principle, suggesting limitations in applying these principles to viscous fluid dynamics.
- Participants discuss a book that claims to address fluid dynamics from an action principle perspective, while expressing skepticism about its credibility based on reviews.
- There is mention of using differential forms as an alternative approach that may successfully derive Navier-Stokes equations.
Areas of Agreement / Disagreement
Participants express differing views on the applicability of action principles to fluid dynamics, with some suggesting limitations while others propose alternative methods. The discussion remains unresolved regarding the effectiveness of the mentioned resources and approaches.
Contextual Notes
Participants highlight the challenges in deriving certain equations from action principles, indicating a dependence on specific assumptions and definitions within the field of fluid mechanics.