Stable Underlying Equations for Constrained Hamiltonian Systems

Stable Underlying Equations for Constrained Hamil- tonian Systems

Constrained Hamiltonian systems represent a special class of differential algebraic equations appearing in many mechanical problems. We survey some possibilities for exploiting their rich geometric structures in the numerical integration of the systems. Our main theme is the construction of underlying equations for which the constraint manifold possesses good stability properties. As an applica...

Symmetric multistep methods for constrained Hamiltonian systems

A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitraril...

Symplectic Integration of Constrained Hamiltonian Systems

A Hamiltonian system in potential form (H(q, p) = p'M~ 'p/2 + E(q)) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in R" . In this paper, methods which reduce "Hamiltonian differential-algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parametrizations...

Symplectic Numerical Integrators in Constrained Hamiltonian Systems

Recent work reported in the literature suggests that for the long-time integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic (or canonical) structure of the ow. Here we investigate the symplecticness of numerical integrators for constrained dynamics, such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limi...

Incomplete Dirac reduction of constrained Hamiltonian systems