Numerical Algorithms 0 ( 1998 ) ? { ? 1 Position Versus Momentum Projections forConstrained Hamiltonian Systems

We study the eeect of position and momentumprojectionsin the numericalintegrationof constrained Hamiltonian systems. We show theoretically and numerically that momentum projections are better and more eecient. They lead to smaller error growth rates and aaect the energy error much less, as they deene a canonical transformation. As a concrete example, the planar pendulum is treated. Let the Hamiltonian H(q; p) (with @ 2 H @p@p nonsingular) be deened in a 2N-dimensional phase space and impose K (irreducible) position constraints (q) = 0. The arising dynamics are usually described by the following diierential algebraic equation