00867nas a2200121   4500008004100000245005700041210005000098260001800148520049700166100002500663700002100688856003600709       2003                        en  d00aOn the local structure of optimal trajectories in R30 alocal structure of optimal trajectories in R3  bSISSA Library3 aWe analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.1 aAgrachev, Andrei, A.1 aSigalotti, Mario  uhttp://hdl.handle.net/1963/1612