Book on discrete mechanics (particularly interested in Lagrangian)

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SUMMARY

The discussion focuses on resources for learning discrete mechanics, specifically the derivation of discrete Euler-Lagrange equations by extremizing the action in a 3D lattice context. Users recommend several papers and a book titled "Discrete Hamiltonian Systems" by Calvin Ahlbrandt, as well as various online resources that provide foundational knowledge in Lagrangian mechanics. Notably, traditional texts like Gregory and Goldstein do not cover discrete mechanics, highlighting the need for specialized literature in this area.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with discrete systems and lattice structures
  • Knowledge of variational principles in physics
  • Basic proficiency in mathematical analysis and differential equations
NEXT STEPS
  • Read "Discrete Hamiltonian Systems" by Calvin Ahlbrandt
  • Study the derivation of discrete Euler-Lagrange equations
  • Explore the provided papers on discrete mechanics for advanced insights
  • Investigate variational methods in discrete systems
USEFUL FOR

Researchers, physicists, and students interested in advanced mechanics, particularly those focusing on discrete systems and the application of Lagrangian principles in non-continuous frameworks.

JD_PM
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Hi.I am looking for a book to learn about discrete mechanics (i.e. working in a 3D lattice instead of ##n## generalized coordinates).

I am particularly interested in how to derive the discrete E-L equations by extremizing the action.

I have checked Gregory and Goldstein but they do not deal with it.Thank you :smile:
 
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While not a book, I found these papers:

https://page.math.tu-berlin.de/~bobenko/papers/1999_Bob_Sur_EP.pdf

https://engineering.purdue.edu/ME564/Notes/I01_Lagrange.pdf

https://www.sciencedirect.com/science/article/pii/089812219090210B

https://arxiv.org/abs/math/0506299

and this PDF on Lagrangian Mechanics (continuous only) as a useful reference:

http://academics.smcvt.edu/abrizard/Classical_Mechanics/Notes_070707.pdf

and lastly, this book on Discrete Hamiltonian Equations:

https://www.barnesandnoble.com/w/discrete-hamiltonian-systems-calvin-ahlbrandt/1103784880
 
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