As President Reagan ends the first year of his second term, authors are scrambling to finish books for publication next spring about his administration and its people.

Foremost among them is David A. Stockman's memoir, "The Triumph of Politics," describing his rise to director of the Office of Management and Budget and his turbulent years in that post. Stockman's book is to be published by Harper & Row this spring, and friends say that the manuscript is full of revelations about Reagan and his advisers.

Other publishers are counting on a renewed interest in Reagan when Stockman's book is published.

Edward J. Rollins, the president's 1984 reelection campaign manager and former White House political director, is writing "Rawhide: An Inside Look at the Reagan White House," to be published by Simon and Schuster in late February. Rollins said he is coauthoring the work with Joe Scott, political editor of the Los Angeles Herald Examiner.

The title "Rawhide" is borrowed from the Secret Service code name for the president. Rollins, now a political consultant, said he is writing about how the White House works, about Reagan's successes in comparison to the troubles of his four immediate predecessors and why he thinks Reagan was successful in taking his case to the American public through the news media.

Rollins said he thinks that the last president with such talents was John F. Kennedy and that he hopes to explain how Reagan and his White House team worked through the fifth year of his presidency.

Owen Ullman, White House correspondent for Knight-Ridder Newspapers, is writing a biography of Stockman for David I. Fine Inc. of New York. Titled "Stockman: The Man, The Myth, The Future," the book is scheduled for publication this spring.

Ullman said he is writing an "unauthorized biography" that will chronicle Stockman's roots, how Stockman came to power and his role as one of the first in the "baby-boom" generation to take a seat around the Cabinet table. Ullman said he also is writing about the young people Stockman brought with him into government: a group that grew up during the Vietnam war, college demonstrations and the growth of the Great Society.

Two long-term Reagan books are also in progress.

Edmund Morris, author of "The Rise of Theodore Roosevelt," is writing an official biography to be published by Random House in 1991. Lou Cannon of The Washington Post, author of two Reagan biographies, is writing a book on the Reagan presidency for Simon and Schuster, scheduled to appear in 1990. Aiming an Ax at Budget

*Stockman's successor, James C. Miller III, has cooked up a host of controversial budget cuts in the fiscal 1987 budget that goes to Congress in February, including plans to sell some federal entities such as the electric power generating networks and the Naval Petroleum Reserves.

Miller's goal is to reduce the projected $194 billion deficit for fiscal 1987 to the $144 million required by the Gramm-Rudman-Hollings law.

Miller also is preparing to send to Congress many of the budget proposals that Stockman tried last year but that died on Capitol Hill, such as abolishing Amtrak and the Small Business Administration.

Informed officials say that Reagan's Cabinet has reacted with unusual calm to these deep cuts. One reason is that chief of staff Donald T. Regan warned the Cabinet that any cuts they reject must be replaced by others of equal magnitude.

Another reason: Many Cabinet members assume that Congress will swiftly reject the Reagan cuts once again, so they are not wasting time fighting over them.

"You're going to come forward with this absolutely Draconian budget," one Cabinet member said. "It's not going to be dead on arrival, it's going to be laughable on arrival."