CAPT OF A GULFSTREAM CPR JET A PENETRATED A PROHIBITED AIRSPACE DURING CLB AFTER DEP RESULTING IN ATC INTERVENTION AND UNITED STATES GOV OFFICIAL INVESTIGATION. THE RPTR STATES THAT THE ERROR WAS DUE TO THE DELAY IN PROPER MODE SETTING OF THE FMC SYS WHEN ATTEMPTING TO TURN THE ACFT TO THE REQUIRED HEADING.

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AT APPROX XX55 UTC GULFSTREAM UNINTENTIONALLY PENETRATED THE AIRSPACE OF P-56. THE FOLLOWING FACTS ARE THE BEST RECOLLECTION OF THE EVENTS THAT LED UP TO THIS. THE FO WAS THE PF AND I WAS PNF. CLRNC WAS RECEIVED FROM CLRNC DELIVERY AT APPROX XX05 UTC. CLRNC WAS CPR CLRED TO BURBANK VIA THE NOISE ABATEMENT PROCS; MAINTAIN 5000 FT. THE CREW DISCUSSED THE DEP REQUIREMENTS; MAKING SURE BOTH PLTS KNEW THE REQUIRED TRACK AND ACFT CONFIGNS; AND ALTS; PLUS REVIEW THE NEED TO STAY OVER THE POTOMAC RIVER FOR NOISE ABATEMENT AND TO MAINTAIN OUTSIDE OF P-56. AFTER DEP; HE; FO; TURNED THE ACFT APPROX 330 DEGS TO STAY OVER THE RIVER. AFTER PASSING 1500 FT HE THEN CHANGED THE BENDIX EFIS FLT DIRECTOR FROM GAR MODE TO HEADING TO MAKE THE TURN TO APPROX HDG 270 DEGS WHEN PASSING THE MEMORIAL BRIDGE. AT THIS TIME THE FLT DIRECTOR COMMAND BARS STOWED FROM SIGHT. NOT BEING HIS PRIMARY ACFT HE TOOK SEVERAL SECONDS (10-15 SECONDS) TO FIND THE HEADING SELECTION BUTTON AND SELECT IT BACK TO HEADING. THIS TIME OF THIS DISTR PLUS A WIND FROM THE W AT APPROX 30-40 KTS DELAYED THE TURN OF THE ACFT TO THE HEADING NECESSARY TO FOLLOW THE POTOMAC RIVER COURSE. THEN HAD TO RELOCATE THE RIVER AND BY THIS TIME THE ACFT HAS MOVED INTO THE AIRSPACE P- 56. ATC ISSUED A L TURN OF 20 DEGS AS THE ACFT WAS ALREADY BEGINNING ITS TURN BACK TO THE W. ATC THEN REQUESTED THE PLT TO CALL TRACON AND INFORM THEM AS TO THE UNINTENTIONAL PENETRATION OF P-56. THE CALL WAS MADE AND HE TALKED TO A CTLR AND PROVIDED HIM WITH THE DETAILS OF THE EVENT. LATER IN THE FLT HE WAS INSTRUCTED TO CONTACT AN OFFICIAL OF THE UNITED STATES GOV AS TO THE EVENT. ARRANGEMENTS WERE MADE TO MEET THE AGENTS AT BURBANK WHEN THE ACFT ARRIVED. HE PROVIDED THE AGENTS THE REQUIRED INFO AT THE FBO HANGAR. THE MAIN REASONS FOR THIS INCIDENT ARE BELIEVED TO BE THE FOLLOWING. 1) THE DESIGN OF THE FLT DIRECTOR SWITCHING REQUIREMENTS. 2) THE CREW'S DISTR WHILE SOLVING THE FLT DIRECTOR MALFUNCTION. 3) THE CREW'S DIFFICULTY IN SEEING THE RIVER WHILE CLBING OUT AT A VERY NOSE HIGH ATTITUDE NEEDED FOR NOISE ABATEMENT. 4) THE CREW'S RELIANCE ON THE FLT INSTRUMENTATION INSTEAD OF VISUAL PILOTAGE. THE CREW KNEW OF THE REQUIREMENTS OF P-56 AND WAS FLYING THE ACFT AS TO COMPLY WITH THAT REQUIREMENT UNTIL THEY BECAME DISTRACTED WITH A SIMPLE FLT NAV PROB. THE TIME SPENT SOLVING THAT PROB COUPLED WITH THE ABOVE CONTRIBUTING FACTORS RESULTED IN THE UNINTENTIONAL PENETRATION OF P-56.