## Symplectic Integration Of Constrained Hamiltonian Systems (0)

Citations: | 46 - 10 self |

### BibTeX

@MISC{Leimkuhler_symplecticintegration,

author = {B. Leimkuhler and S. Reich},

title = {Symplectic Integration Of Constrained Hamiltonian Systems},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

. A Hamiltonian system in potential form (H(q; p) = p t M \Gamma1 p=2 + F (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 n . In this paper, methods which reduce "Hamiltonian differentialalgebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint-invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically. Key words. differential-algebraic equations, constrained Hamiltonian systems, canonical discretization schemes, symplectic methods AMS(MOS) subj...