NAMar 5, 2009
Error analysis of variational integrators of unconstrained Lagrangian systemsGeorge W. Patrick, Charles Cuell
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future symmetry.
NAMar 5, 2009
On converting any one-step method to a variational integrator of the same orderGeorge W. Patrick, Raymond J. Spiteri, William Zhang et al.
In the formalism of constrained mechanics, such as that which underlies the SHAKE and RATTLE methods of molecular dynamics, we present an algorithm to convert any one-step integration method to a variational integrator of the same order. The one-step method is arbitrary, and the conversion can be automated, resulting in a powerful and flexible approach to the generation of novel variational integrators with arbitrary order.