Numerical integration of constrained Hamiltonian systems using Dirac brackets

Numerical integration of constrained Hamiltonian systems using Dirac brackets

We study the numerical properties of the equations of motion of constrained systems derived with Dirac brackets. This formulation is compared with one based on the extended Hamiltonian. As concrete examples, a pendulum in Cartesian coordinates and a chain molecule are treated.

Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric met...

Incomplete Dirac reduction of constrained Hamiltonian systems

Integration of Twisted Dirac Brackets

Given a Lie groupoid G over a manifold M , we show that multiplicative 2forms on G relatively closed with respect to a closed 3-form φ on M correspond to maps from the Lie algebroid of G into T ∗M satisfying an algebraic condition and a differential condition with respect to the φ-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to φ-twist...

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...