Geometric Integration of Degenerate Lagrangian Systems
The Geometric Numerical Integration literature describes numerous structure-preserving algorithms for canonical Hamiltonian and regular Lagrangian systems. Noncanonical Hamiltonian and degenerate Lagrangian systems, on the other hand, are rarely discussed. Such systems play an important role in reduced charged particle dynamics like the guiding centre model, population dynamics like the Lotka–Volterra model, or nonlinear oscillators. This is a short overview of the issues that arise when discretising such systems and a discussion of possible strategies for their structure-preserving integration.
© Michael Kraus. Last modified: March 10, 2023.