Gauge independent Hamiltonian reduction of constrained systems

Gauge Independent Lagrangian Reduction of Constrained Systems

A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered. On leave of absence from S.N.Bose National Centre for Basic Sciences, Calcutta, India. E-mail: [email protected]

Incomplete Dirac reduction of constrained Hamiltonian systems

Geometric reduction of Hamiltonian systems

Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector Π on M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical ideas of Dirac (Dirac reduction) and more modern theory of J. Marsden and T. Ratiu, but our method leads to formulas that allow for an explicit calculation of the...

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...