Domain of Free Trajectories on Invariant Manifolds

Abstract

Suppose that there exists an invariant manifold M, with dimension k < n, which the representative point q of a CDS cannot leave under the action of an admissible control. It is interesting to derive conditions under which there exists an open (in the interior metric of M) submanifold D ⊂ M, also of dimension k, in which any two points q₀ ∈ D and q1 ∈ D can be joined in an admissible way by a trajectory lying entirely in D. We call this submanifold D ⊂ M the domain of free trajectories on the invariant manifold M, in analogy with the notion of the domain of free trajectories which was examined in Sec. 9.