INAUGURATION '85. Reagan's goals: growth and peace. `I, Ronald Reagan, do solemnly swear . . .' -- the President embarks on his second term

Duly sworn in as President of the United States for a second term, Ronald Reagan is poised to pursue two broad objectives which, if achieved, will enable him to leave office claiming a solid legacy and an honored place in presidential history: Keeping the US economy moving on a stable, forward path.

Reaching an arms reduction agreement with the Soviet Union and heightening the prospects for long-term peace.

As the President begins his second term, the outlook for achieving these goals is reasonably good, in the opinion of many political and diplomatic observers. The economy, though it has slowed, is expected to grow at a respectable rate. Mr. Reagan has already laid the ground for a resumption of arms control talks with the Russians and picked a new negotiating team. Recent polls indicate that most Americans are optimistic and confident about the future, highly approving of the President's leadership, and even more favorably disposed to the government in Washington. This adds to Mr. Reagan's ability to mobilize public support for his policies.

Even Democrats, despite the President's lame-duck status and their criticism of his passive strategy on the federal budget, do not rule out the possibility of a productive second term.

``Reagan could be more successful in his second term than his first because he will be sensitive to history in terms of reducing confrontation with the Soviet Union and making things a bit easier for the poor,'' says one prominent Democratic leader.

But there clearly are economic and political obstacles that could thwart achievement of the President's goals: a soaring budget deficit that could undermine economic growth; an increasingly independent Congress which, with its eyes on the 1986 election and the 1988 political succession, does not feel beholden to a second-term president; pushing and hauling within the administration over US arms policy; and a potential political vacuum at the White House brought on by a breathless spate of staff changes.

For the moment, affairs of state are suspended as Washington revels in a host of inaugural festivities, culminating today in the public inaugural ceremony at the Capitol, the traditional parade down Pennsylvania Avenue, and nine inaugural balls. Yesterday, Jan. 20, which the Constitution establishes as the official start of the presidential term, Vice President George Bush and Mr. Reagan took the oath of office in a simple and moving ceremony at the White House. Later in the day, unfailingly sensitive to what dominates the attention of the American public, Mr. Reagan was scheduled to flip the coin to determine who kicked off the Super Bowl XIX football game, an event to be beamed by satellite to site of the game and aired live on television.

For all the President's keen political instincts, some political experts see stalemate ahead between Congress and President. Mr. Reagan even now conveys the impression to some in this capital that he is detached from governing, without that burning passion which drives a president in his first term. The President has not, for instance, articulated a domestic agenda or shaped a central strategy.

Based on his reelection campaign themes and preoccupations since Nov. 6, Mr. Reagan will try to reduce the size of government, cut the rate of federal spending, and reform the tax system. But many political observers believe the President is now less preoccupied with domestic affairs and is not greatly concerned about the deficit, though he will be forced by political if not economic considerations to deal with it.

``If the President had his `druthers,' he would spend more time on foreign policy,'' says Norman Ornstein of the American Enterprise Institute. ``He would like to divert attention away from the domestic situation, but to do this he has to be sure the deficit does not explode in his face. So, like it or not, defusing that time bomb has to be a major priority.''

Although as yet there is no clear presidential strategy, those who have closely watched Reagan's political career over the years see consistency in his pragmatic style of governing and shrewd politics in his laid-back approach since the election. The President has not been proclaiming a second-term ``mandate,'' for instance, despite his massive popular victory in 1984. He is not doing so, say seasoned observers, because he knows he can achieve his second-term objectives only by working with Congress members and must be careful not to alienate them.

Mr. Reagan's campaign promises not to touch social security or increase taxes, as well as his declared belief that economic growth will take care of the deficit, make it awkward for him to take the initiative on a deficit-reduction plan, say anaylsts. Hence he is waiting for Congress to make its moves before he steps in to bargain, compromise, and declare victory. He may even accept a tax increase, but not until he gets to the bottom line on spending cuts.

``His strategy now is understandable,'' says Isabel V. Sawhill, an economist at the Urban Institute. ``If your goal is not to decrease deficits -- and he's not concerned about that -- but to shrink government, achieve arms control, and get tax reform, he's got a good shot at all three. Now he's just standing back and letting others accomplish his objective of reducing spending.''

In his final four years the President also will continue advocating such social goals as a constitutional ban on abortion, prayer in the schools, and tuition-tax credits. One of his early post-inauguration public appearances this week will be to speak at an antiabortion rally near the White House. But, with hardline conservative Edwin Meese III moving from the White House to the Justice Department, and given the divisions in Congress on these issues, the President is not expected to push social issues actively.

However, the potential appointment of conservatives to the US Supreme Court could set the judiciary in the direction Mr. Reagan seeks.

It is because relations with Congress, especially with the moderates, will be so important in the second term that the White House staff changes are seen to be critical. Outgoing chief of staff James Baker III and other aides are credited with masterful understanding of congressional politics. Incoming chief of staff Donald Regan is said to lack political skills.

``To lose the one person who was best in carrying out strategy, with no one in charge yet and things in flux, is a dangerous move,'' says Mr. Ornstein.