A reinforced battalion of crack U.S. paratroopers parachuted into the Egyptian desert today after a nonstop flight from the United States in the most ambitious test of the 2-year-old U.S. Rapid Deployment Force.

The airdrop, the first exercise of a series of joint Egyptian-U.S. military maneuvers here called Operation Bright Star 82, coincided with the conclusion of the 40-day Moslem mourning period for slain Egyptian president Anwar Sadat who had helped plan the excerises aimed at training U.S. and Egyptian troops to react to any threat in this volatile region.

Within hours after the airdrop of 865 men from the 82nd Airborne Division and their 180 tons of equipment into a preselected desert landing zone 40 miles northwest of Cairo, Jihan Sadat, Sadat's widow and her four children, accompanied by the self-proclaimed shah of Iran, Reza Pahlevi, visited the temporary tomb of the late Egyptian president at the tomb of the unknown soldier in the Cairo suburb of Nasr (Victory City) for private prayers.

The prayers were said over Sadat's temporary tomb, 200 yards from the reviewing stand where he was shot to death while watching a military parade Oct. 6. His successor, President Hosni Mubarak, delivered a speech urging Egyptians to join forces for national reconciliation and to bring about the sort of economic and industrial reforms that might stifle the Moselm fundamentalist terrorism that led to Sadat's assassination.

"The world is watching us closely, fearing that the causes for which Sadat lived may be threatened by his death," the Egyptian president said in a eulogy delivered in the hall of his party's central committee as the desert exercises got underway. "But words are not enough. We must honor the memory of Sadat by translating his dream and hope into action. This is our challenge, we must not fail."

The exercise, part of a month-long operation that involves 4,000 Americans in Egypt and 2,000 in exercises in Sudan, Somalia and Oman, had been preceded by a 10,000-foot night airdrop of a team of Special Forces Green Berets and an Air Force Command Control Team to secure the half-mile by quarter-mile landing zone.

Today at 9 a.m. local time, after a squadron of A10 Thunderbolt II tactical fighter bombers had staged 10 minutes of runs over the sandy drop zone, a flight of two dozen C130s and C141 Starlifters -- six of which had flown with 602 paratroopers of the 82nd Division's second battalion, 14 hours nonstop, from Ft. Bragg, N.C. -- swooped in over the desert to disgorge their men and materiel in a near perfect parachute drop that lasted barely six minutes. They then linked up with a battalion of the mechanized 24th Infantry that had flown into Egypt, with its M60 tanks and M113 armored personnel carriers coming by sea.

Part of today's 865-man force flew to Egypt from unidentified staging bases in Europe.

After watching the airborne drop, flanked by high-ranking Egyptian officers in a reviewing stand a mile from the drop zone, Lt. Gen. Robert C. Kingston, the head of the Rapid Deployment Force said, "It was a good excerise, a good drop."

He said that while in an emergency it would take four full days for a similiar force to be flown to the area, he could put one airborne battalion into the region "within 24 hours."

The significance of the exercise was that for the first time since the Rapid Deployment Force was created March 1, 1980, it had managed to fly a full combat contingent overseas and land it ready to fight with all of its provisions and equipment, including 105mm howitzers, quarter-ton jeeps with antitank missiles and its new six-wheel, all-terrain Gamma Goat vehicles.

Only one vehicle, a Gamma Goat, was damaged in the drop when its parachute failed to open properly, and a major, whom the military refused to identify immediately, suffered a broken hip, and two other paratroopers were slightly injured in landing.

The marathon flight was deemed a successful test of the Rapid Deployment Force's newly developed scheme to avoid "jet lag" for its fighting troops during long flights overseas.

U.S. Military officials here said the airborne troops were "programmed" for the transatlantic flight by gathering them early at Ft. Bragg where they were quickly put on Egyptian time and sleep and feeding schedules. In the air last night they were given a high-carbohydrate diet as soon as they boarded their planes, then allowed to go to sleep for eight hours on litters while the plane's temperature was raised to 80 degrees to induce sleep. Hours before reaching Egypt they were awakened, fed a high-protein diet of ham-and-egg omelets and fruit, rigged for parachuting and dropped.

The airborne and mechanized infantry battalions will spend the next week in small-unit training operations with their Egyptian counterparts and exchange tactics and compare equipment with Egyptian units. Later this month the 4,000-man U.S. force will join a similiar force of Egyptians in two days of maneuvers on the Western Desert that will be highlighted by a live, low-level bombing run by a squadron of B52 bombers flying nonstop out of Minot Air Force base in North Dakota.

Along with the bilateral exercises the U.S. forces are staging in Egypt, they will also be holding lesser operations in Somalia, the Sudan and Oman.