The image lingers: Sen. Edward M. Kennedy, his features drawn into a look of apparent disdain, dances around the podium at Madison Square Garden on the last night of the Democratic convention, evading President Carter the way a matodor twirls away from a bull -- denying the president the news-magazine cover shot of party unity he sorely wanted.

It is an image both Carter and Kennedy would like to erase, though not necessarily for the same reasons. So Kennedy is now beginning an intensive final month of campaigning of behalf of the Carter-Mondale ticket.

"A year ago when I began my campaign, I had it planned down to the day," Kennedy said on Wednesday to a group of New York lawyers who support Carter."I planned that on Oct. 8, I would be in New York campaigning for the presidency. And here I am -- for President Carter."

Earlier that day, Kennedy taped a series of television and radio ads for Carter, some of them specifically aimed at black and Hispanic voters. In the next few weeks, the senator will make appearances in virtually all the big states that Carter must win in order to defeat Republican candidate Ronald Reagan in November. The Carter forces count on using Kennedy as a big gun, an Ultimate Weapon who can rally apathetic minorities and disaffected liberals against Reagan.

"He has an image and a credibility we can't duplicate," acknowledged Carter-Mondale campaign chairman Robert S. Strauss. "Wherever traditional Democrats are, whether New Jersey or Illinois or Pennsylvania, he has a credibility that we need."

The Carter campaign's desire to bring Kennedy into the fold is so great that Carter has agreed to join in a series of fund-raisers to help eliminate Kennedy's $1.7 million campaigh debt from the primaries.

But if Carter has compelling reasons to want to blot out the notion that Kennedy does not truly support him, so does Kennedy. In the one interview that he has granted since the convention, Kennedy made it clear that he still would like to be president some day. At the convention, Carter spoke of Kennedy's "great future" in the Democratic Party. But those future prospects could be diminished if Kennedy -- as he did on the podium -- continues to give the impression that he feels ambivalent about supporting an incumbent Democratic president against a strong GOP challenger.

Aides to both Kennedy and Carter maintain that the shotgun marriage is nonetheless a happy one. Both sides point to the fact that Jack English, who coordinated Kennedy's primary campaigns in New York and New Jersey and was his convention floor manager, is now a member of the Carter campaign's policy committee and is handling the Carter-Kennedy liaison. Strauss said English has been a "tremendous help."

But much of Kennedy's campaign effort is being done on his own terms. The ads he taped on Wednesday, for example, were produced by his own media specialist, David Sawyer, rather than by Carter's media man, Gerald Rafshoon, who produced anti-Kennedy ads during the primaries that subtly attacked the senator's character and reportedly angered Kennedy.

In addition, Kennedy has no intentions of mounting a frontal assault on independent candidate John B. Anderson, who is believed to be siphoning votes from Carter in key states like New York.

"The senator consistently said during the primaries that he thought Anderson was running a creditable campaign," said Dick Drayne, Kennedy's press aide. "He told the president his position was that Anderson should be included in the presidential debates. Kennedy's feeling about Anderson is that he has said he thinks Jimmy Carter is the best way to beat Ronald Reagan. He has not specifically attacked Anderson."

Said Strauss, "We don't need Kennedy to attack Anderson. Look, there are some differences between Carter and Kennedy, very strong differences on some issues. No one tries to tell Sen. Kennedy what to say."

Next week, Kennedy will appear with Carter in Boston, New Jersey and Washington, and make a solo trip to Detroit and Wisconsin on behalf of Carter. One of the Washington appearances is a joint fund-raiser.

The following week, Kennedy makes a trip to Texas. Kennedy aides say the Carter forces specifically requested that the senator make this trip alone. Kennedy's clout among Mexican Americans, who make up an important part of the Texas electorate, is seen by the Carter campaign as vitally necessary for the president to carry the state and its crucial 26 electoral votes.

Kennedy will also appear in Cleveland, and has been asked to hold open the last week before the election for as-yet unscheduled activities, which might include a trip to California. Kennedy has already made an unsuccessful appeal to win the backing of New York's Liberal Party -- and its line on the Nov. 4 ballot -- for Carter instead of Anderson.

"I believe his motives are very simple and straightforward, and that he believes we should elect a Democrat and not Ronald Reagan," Strauss said of Kennedy. "The senator has been around for a long time. He remembers back in 1960 when his brother ran, he didn't see Hubert Humphrey holding back."