Relational evolution of observables for Hamiltonian-constrained systems

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...

Incomplete Dirac reduction of constrained Hamiltonian systems

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...

Fuzzy Relational Matrix-Based Stability Analysis for First-Order Fuzzy Relational Dynamic Systems

In this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.In the first approach, the equilibrium point of the system is one of the centers of the related membership fu...