The helicopter swooped low over the woodlands, giving Sen. Edward M. Kennedy (D-Mass.) his first look at a New Hampshire sunset since his neighbors gave him his first and most crushing presidential primary defeat two years ago.

Next time, he vows, he will work harder at building the "special relationship" with New Hampshire voters that politics in that state requires. If he runs.

He is in the state this time as featured attraction at two fund-raisers for the cofounder of the Draft Kennedy in '80 movement, the politically redoubtable Dudley Dudley, who is seeking reelection to the state executive council.

"I am grateful to come up here," Kennedy laughingly tells her audience, "for someone who snookered me into running in the first place."

Although Dudley was co-founder of draft Kennedy in 1980, she later explains why she is not for Kennedy in 1984.

"What the Democrats need most of all now is a presidential candidate who can win," Dudley said after the last fund-raiser and as Kennedy's helicopter headed toward Hyannisport, Mass. She said she appreciates Kennedy's visit, but adds:

"Four more years of Ronald Reagan will be a disaster. We need a winner . . . . I just don't think Kennedy can win it."

So she is looking elsewhere -- at former vice president Walter F. Mondale, Sens. John Glenn (Ohio), Gary Hart (Colo.), Alan Cranston (Calif.) and other Democrats, she said.

She is looking to see what she can do to help make one of them the next president because of serious doubts that Kennedy can be elected even if he wins the 1984 Democratic presidential nomination.

The front-runner must prove he can win. That is the paradoxical challenge that awaits Kennedy because he may not run for president again.

He is well ahead of other Democrats in the early polls, in which he scores in the 40 percent range, while the rest are in the teens and lower. But he was well ahead of President Carter in 1979 when those around him were telling Kennedy that the nomination was his, if he decided to run. So he thought about if, but never how or why.

And the big contest of 1980 quickly degenerated into a question of whether Kennedy would run his own presidential candidacy into the ground before his campaign organization did it for him. It was a dead heat.

"I learned a lot in 1980," Kennedy said. "A lot about myself, a lot about the country, a lot about what a run for the presidency means. Hopefully I'm still smart enough to learn and learn profoundly from it.

"I learned to rely on my own instinct to a greater degree; to respond to my own sort of gut sense. In the end, I think I performed better as a candidate -- took on a . . . sense of direction . . . . But it got tripped off on the wrong foot. I was responsible for that.

" . . . I had campaigned with my brother, President Kennedy, and with Robert Kennedy. But it's a different experience when you're a candidate yourself," he said.

Next time, Kennedy has vowed that everything will be done right. If he runs.

As part of the preparation for 1984, he flew to California and New Mexico recently for a hectic weekend of campaigning for fellow Democrats.

He went to California, primarily to appear at an AFL-CIO dinner with Gov. Edmund G. (Jerry) Brown Jr., the Democratic Senate candidate.

There, in the lavish ballroom of the Century Plaza Hotel, the state's labor leaders and politicos bowed their heads for the invocation.

"Dear Lord," the Rev. John Simmons prayed, "deliver us from hot air."

The evening proved memorable, as Brown never showed up to give his campaign speech and Kennedy delivered a strong but not strident address.

Kennedy has learned to speak without shouting. He no longer tries to fill the hall with his voice, which in 1980 was good theater but shrill on the evening television news, where most Americans got to know him.

Moreover, in the California speech, Kennedy was not only good but gracious, despite political strains.

Last summer, he angrily warned Brown and Cranston that he might not campaign for Brown because the governor was endorsing fellow Californian Cranston for president.

But Kennedy came off looking petty when that exchange became public, and so he went to California to extol Brown's virtues at every stop despite Brown's inexplicable absence at the labor dinner.

At times, Kennedy's performances are not so strong. Campaign managers explain away candidates who lack oratorical flair: "He's really great in small groups," they say.

The line on Kennedy is that he is better in amphitheaters than in living rooms.

When the groups are not large, when the adrenaline is not flowing, his mind seems adrift. He often serves up bromides, and even these tend to emerge disjointed and buried in a morass of "ahs" and "ers" and "uhs."

Most candidates, when they feel the need for self-improvement, study videotapes of their major speeches to learn how to do better; Kennedy would be better off watching tapes of his performances in kaffeeklatsches. They would show that he makes it seem that even the most predictable question has caught him unaware.

The same is true of interviews. A reporter, whom Kennedy knew was working a story on his probable presidential campaign, asked about concern of some of his former supporters, such as Dudley Dudley, about whether he can ever win a presidential election.

Kennedy begins answering by saying he is concentrating on his Senate reelection campaign this year. Then slowly, hesitantly, he inched along, as if negotiating a slippery political slope.

"I have every intention of being actively involved in the party, in the Senate, in the future. And I intend to continue to be a constructive force, a positive force, a light force and a force for practical solutions to the problems we're facing here at home and around the world. The form and shape that comes in has to be decided down the road," he said.

"But I have a very keen awareness, understanding as to my own mind -- now there are long pauses -- what I want to, ah, kind of, ah, examine, what I want to be and the issues I want to be involved in.

"Now, how other people are going to perceive various actions, other kinds of actions, will obviously be speculated on. And I'm -- I don't make any -- the fact that over a long period of time, almost ever since I have been in public life and public office, and there's very little that I can do to affect it. You know, it will continue as long as I am in public life, I'm sure."

Kennedy generates a larger audience and more enthusiastic response than any other Democratic presidential hopeful. He also generates more negative feeling.

When he appeared in Missouri for Senate candidate Harriett Woods, he attracted a sizable crowd at a fund-raiser.

But the next day, a radio call-in show was dominated for an hour by callers angrily denouncing Woods for her ties to Kennedy. It left Woods' supporters muttering that it had done more harm than good.

Ability to be elected is the concern raised about Kennedy. It has been heard many times. Pundits said Reagan was too far to the right; some now say Kennedy is too far to the left.

But ideology is a small part of the question. Kennedy's real problem is rooted in doubts about his personal character, which surfaced in 1980 when voters had to focus on whether they wanted Kennedy to be their next president.

Patrick Caddell spotted the depth and intensity of those doubts when he was polling for President Carter and mapping strategy on how to defeat the Kennedy challenge.

Doubts arise from the 1969 incident at Chappaquiddick, where Mary Jo Kopechne died in a car driven off a bridge by Kennedy, who then did not summon help or report the accident until the next day. And doubts arise from other personal problems, including the breakup of his marriage.

Caddell is again measuring depth and intensity of voters' feelings about Kennedy's personal character. But this time he is polling for Kennedy, and his findings will be a major factor in whether Kennedy decides to run again.

Caddell also is measuring the impact of the unusual, intensely personal five-minute television advertisements that Kennedy has been airing in Massachusetts and that are seen by most New Hampshire voters.

Officially, the ads are part of Kennedy's Senate reelection campaign; in fact, they are central to a Kennedy presidential run in 1984.

The ads feature people who have known Kennedy for years talking about the pain and suffering he has experienced. They dwell on his son, Teddy, who lost a leg to cancer, the assassinations of his brothers and how he had to pull things together for their families and his.

"He's not a plaster saint," one ad speaker said. "He's not without fault."

Kennedy and his advisers apparently do not believe they can ever change voters' minds about Chappaquiddick. But they hope they can show a compassionate, much-suffering side of Kennedy. It is crucial to any hopes he has of being president.

A New Hampshire state senator tells of his wife, whom he describes as a hater of the Kennedys, particularly Edward. But she was deeply moved by the ads. "I was stunned," he said, "when she said to me the other day, 'You know, there's more to him than I ever realized.' "

If Kennedy's surveys show significant change in public perceptions, he will be campaigning for president in earnest next year. But if they show that the problem of his personal character remains unimproved and insurmountable, influential people are prepared to urge him strongly not to do it.

If he does run, he will have a streamlined campaign organization, with clearly defined lines of responsibility, his advisers vow. It will feature several major additions and deletions.

It will be headed this time by Kennedy's newest Senate administrative assistant, Lawrence Horowitz, at 37 inexperienced in presidential politics but close to the candidate and dedicated to execution of detail.

Directing daily political operations will be New York attorney John F. English, a veteran of Democratic political wars such as Edmund S. Muskie's 1972 presidential campaign. English engineered Kennedy's major success in his ill-starred 1980 effort, the rout of Carter in the New York primary.

Some of the glitterati of past efforts to recapture Camelot will be missing, however. Stephen Smith, who in 1980 won no plaudits for political or administrative skill as the campaign's commander-in-chief, will carry only the rank of brother-in-law in 1984.

Kennedy now is campaigning only for others. Yet he keeps a schedule more hectic than any of the 1984 presidential aspirants. At the end of a typical three-day, 25-stop weekend trip, he was asked if he knew, deep down, whether he will run for president in 1984.

"No," he said, following with a long pause. "I could make a decision now by not doing some things. But I'm not making that decision."