The adjustment-stabilization method for constrained systems

TL;DR

The paper introduces the adjustment-stabilization method, a new technique for stabilizing all constants of motion in constrained systems, improving numerical accuracy over existing methods that only conserve one integral.

Contribution

It presents a novel adjustment-stabilization method that stabilizes all known first integrals simultaneously, unlike previous methods that only conserve one.

Findings

Effectively stabilizes all known constants of motion.

Improves numerical accuracy in constrained systems.

Post-stabilization is a special case of the new method.

Abstract

For constrained system which has several independent first integrals, we give a new stabilization method which named adjustment-stabilization method. It can stabilize all known constants of motion for a given dynamical system very well instead of the stabilization and post-stabilization methods which only conserves one of all first integrals. Further more, new method can improve numerical accuracy too. We also point out the post-stabilization is just a simplest case of the new method.