We consider a Lagrangian system SIGMA with some additional time-dependent constraints, which are kinematically represented by functions of time which take values in a foliation F of the configuration manifold M. It is shown that the evolution of SIGMA depends continuously on these constraints (with respect to the C0 or weaker topologies) if and only if F satisfies certain orthogonality conditions. Some examples concerning a constrained particle and a rigid body are provided.
ON THE RIEMANNIAN STRUCTURE OF A LAGRANGIAN SYSTEM AND THE PROBLEM OF ADDING TIME-DEPENDENT CONSTRAINTS AS CONTROLS
RAMPAZZO, FRANCO
1991
Abstract
We consider a Lagrangian system SIGMA with some additional time-dependent constraints, which are kinematically represented by functions of time which take values in a foliation F of the configuration manifold M. It is shown that the evolution of SIGMA depends continuously on these constraints (with respect to the C0 or weaker topologies) if and only if F satisfies certain orthogonality conditions. Some examples concerning a constrained particle and a rigid body are provided.File in questo prodotto:
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