Democratic National Convention keynoter Morris K. Udall summoned Democrats tonight to give themselves a "fighting chance" this fall by forgiving each other and uniting against what he called a "radical right" Republican Party.

He departed from his prepared text at the outset to praise Sen. Edward M. Kennedy (D-Mass.) for having waged a "great fight" for which he said the party owed a "debt of gratitude."

While it is easy to win, said Udall, it takes "real class and real gallantry" to lose in the way Kennedy did.

Striking a theme that was echoed by other party leaders in the aftermath of this evening's rules vote, Udall attempted to hold up Republican nominee Ronald Reagan as the great unifier -- of the Democrats.

But the rhetoric on the opening day of the convention was short on the usual advance claims of victory and long on appeals for what Udall called "forgiveness and magnanimity."

"Some folks are already writing Democratic obituaries for 1980," said the Arizona congressman and 1976 challenger to President Carter, an early supporter of Sen. Edward M. Kennedy (D-Mass.) and a bridge between the feuding factions of the party. "I don't pretend that this will be an easy year. But this old Democratic mule isn't that easy to beat. And if we handle ourselves right in these next 72 hours, we can come out of her with a fighting chance to win."

Udall spoke to a half-empty hall, made even barer when the Alaska delegation walked out midway in his speech to protest his stand on the Alaska land bill.

If Udall couldn't rally the Democrats with advance claims of victory, as the Republicans did in Detroit last month, he could -- and did -- hold up the specter of "President Ronald Reagan" as a unifying force.

"If you don't feel all that unified by Thursday," he said, "let me recommend Dr. Udall's Patented Unity Medicine. Take one tablespoon, close your eyes and repeat President Ronald Reagan."

Speaking beyond the delegates to Democratic and independent voters, he attempted to rally them against a Republican Party that he characterized as "dominated by the radical right, urging radical economics at home and belligerent policies abroad."

Udall bore down on what he called the "free lunch" promises of the Republican Kemp-Roth tax cut proposal aimed at stimulating business activity that would, in turn, generate more tax revenues.

"The party of Calvin Coolidge has warned as long as I can remember that we can't spend ourselves rich and that there is no free lunch," said Udall. "And now, here in 1980 . . . they tell us there is a free lunch, that you really can spend yourself rich."

At the same time, Udall lifted a leaf from the Republicans' book by portraying the Democrats -- not the GOP -- as saviors of the free enterprise system.

"Democrats don't just preach competition, we practice it," he said. Franklin Roosevelt, he added, "saved the free-enterprise system and American business has nearly always done better under Democratic presidents."

As for the Democrats, he said they have two courses to follow: the divisive course of 1968, when Hubert Humphrey lost to Richard Nixon, or the course of 1948, when Harry Truman was reelected.

"I suggest the road to follow is the path of forgiveness and magnanimity, and the path of Democrats pulling together, putting our differences behind us for the sake of a better country. If we're going to have some fights this week, so be it. But we should promise there will be no low blows."

Earlier, Udall attempted to make light of the difficulty of writing a traditionally upbeat keynote speech for a party that is trailing so badly. While his Republican counterpart, Rep. Guy Vander Jagt (R-Mich.), had practiced his speech in the forests of Michigan, Udall said he had considered doing his oratorical rehearsals in the Great Dismal Swamp.

In another speech prepared for the convention tonight, Sen. Daniel P. Moynihan (D-N.Y.) characterized the last four years as a time of unprecedented defense expenditure, "fixing," as he put it, "a new direction only just begun in the final year of the previous administration."

He credited the Democrats for having "increased defense spending in each and every one of the past four years [and] commenced a massive return to strategic weapons development," skipping over the fact that this has not been met with universal approval within the party.

But Moynihan also defended the administration's pursuit of a strategic arms agreement with the Soviet Union, excoriating the Republicans for describing the Democratic policy as tantamount to "unilateral disarmament," said Moynihan: "Must we not ask: If a party is this careless with words, can it be trusted with power?"

In denouncing the strategic arms limitation treaty (SALT II) now on a Senate back-burner, the GOP "derides the very quest for nuclear peace," said Moynihan.

In a companion speech on domestic themes, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) evoked the traditional Democratic social concerns and accused the Republicans of unjustly trying to appropriate Franklin D. Roosevelt and his legacy. "No amount of rhetoric can hide the fact that the agenda of the Republican Party, as embodied in [the GOP] platform is reactionary and overly simplistic," said O'Neill.

As Udall and others did, O'Neill made a point of Republican spurning of the Equal Rights Amendment for women. "The Republicans may feel they can lay a claim on Franklin Roosevelt," said O'Neill, "but after their disgraceful about-face on ERA, Eleanor still belongs to us."

New York Gov. Hugh Carey, welcoming the Democrats back to New York City, called the Republicans "diamond-studded demagogues . . . who cares less about the rights of children than they do for the royalties of oil companies" and bristled, too, at their newfound affection for Roosevelt."They didn't fool our grandparents," he said, "and they can't fool us."

In a glancing reference to the open convention fight that the Democrats staged earlier in the evening, Democratic National Chairman John C. White contrasted it with what he called the "slick, contrived and manipulated" convention of the Republicans and added, "If there was ever a closed convention, that was it."