A generalized geometric framework for constrained systems. (English) Zbl 0763.34001

A geometric framework for constrained dynamical systems of the form \(A(x)x'=F(x)\) is presented. The framework is used to describe a general type of first order differential equations on a manifold. In this paper these systems are called linearly constrained systems. A stabilization algorithm is devised and discussed in order to solve the equation of motion. The formalism includes the presymplectic and Lagrangian formalisms as well as higher order Lagrangians. In numerical analysis the system \(A(x)x'=F(x)\) is called a linearly implicit differential algebraic equation (DAE). The stabilization algorithm of this paper consists of the construction of a sequence of manifolds. This is very similar to the recent constructions of Rabier, Reich, and Rheinboldt developed in the numerical analysis literature of DAEs.


34A09 Implicit ordinary differential equations, differential-algebraic equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H05 Hamilton’s equations
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