Classical Book on discrete mechanics (particularly interested in Lagrangian)

[JD_PM]

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

 

[jedishrfu]

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