Lyapunov-Schmidt Method for Dynamical Systems.

Scanning welding heads are introduced through respective openings of a workpiece into the workpiece by respective welding robots. When a laser beam is emitted from a laser beam emitting device, the laser beam is applied to a beam splitter of one of the welding robots, which reflects about 50% of the energy of the laser beam and introduces the laser beam into a scanning welding head. The beam splitter passes the remaining 50% of the energy of the laser beam therethrough. The laser beam that has passed through the beam splitter is reflected by a totally reflecting mirror of another scanning welding head. The scanning welding heads apply the laser beam to respective regions in the workpiece to weld the workpiece.