On the realization of holonomic constraints
The general theorem on the realization of holonomic constraints with the help of elastic forces directed towards the configurational manifold of the constrained system refers to Courant. There exist generalizations of the main result, all assuming that the system in question is conservative. The main result of this paper is that the Courant's theorem is valid without this assumption. More precisely, a free system \((\partial E/\partial \dot r)^ .-\partial E/\partial r=F-N\partial w/\partial r\) with sufficiently large \(N\) and \(W\) having its minimum on the manifold of constraints, is considered. Let \(r_ N(t)\) and \(r_ \infty(t)\) be the evolutions of the free system and the constrained system, respectively. Under certain nonrestrictive assumptions it is proved that for \(0\leq t\leq 1\) \(r_ N(t)=r_ \infty(t)+O(N^{-1})\), \(\dot r_ N(t)=\dot r_ \infty(t)+O(N^{-1/2})\).
scientific article; zbMATH DE number 56386