Despite growing opposition on college campuses to President Reagan's Strategic Defense Initiative (SDI), the Pentagon is having no trouble finding takers for its often lucrative "Star Wars" research contracts.

The issue of whether to take SDI funding has provoked a passionate debate at many universities because of fears that the project may become classified and because of outright opposition to the project.

A group of academic opponents yesterday appeared on Capitol Hill with petitions containing the names of more than 1,300 scientists from at least 21 universities, including 12 Nobel laureates, who have pledged not to accept SDI money.

The petitions state that SDI is "ill-conceived and dangerous," "not technically feasible" and "will only serve to escalate the arms race . . . . "

But in the midst of the controversy, which coincides with diminishing research money from other sources, many engineers and physicists at more than two dozen colleges have accepted SDI contracts while hundreds of others have sent in proposals seeking a piece of what could become the largest source of federal research funds for the next decade.

Scientists seeking SDI funding say that they see no problem with contributing their research to the controversial weapons system since they would be researching the same basic topics regardless. In many cases, these scientists have the stated support of their university administrators and boards of trustees.

One example is Ronald Gilgenbach, a nuclear-engineering professor at the University of Michigan in Ann Arbor, who said he received a $181,000 grant from the Strategic Defense Initiative Office to research laser and electron beam technology. Although his research could eventually be used to make weapons to shoot down enemy missiles, he says that to him it is basic research conducted in the name of scientific inquiry.

"I am doing fundamental research to determine the fundamental laws of nature," he said. "Because SDI is funding it doesn't change the fundamental laws of nature."

In Ann Arbor late last month, the University of Michigan Board of Regents passed a resolution supporting any professor, like Gilgenbach, who chooses to conduct SDI research.

The resolution stated that "scholars who wish "The right to do research should not be infringed." -- University of Michigan regent Thomas Roach to participate in Strategic Defense Initiative research are encouraged to undertake the research" as long as it is in accordance with university rules. University rules prohibit classified research on campus.

"I have no idea whether Star Wars is good or bad, whether it will work or won't work, whether it's in the best or worst interests of our strategic balance," said regent Thomas Roach at a forum on SDI. "But the right to do research should not be infringed."

Scientists leading the the national opposition to SDI research sometimes work out of offices down the hall or across the campus from colleagues who have expressed interest in getting SDI money.

For example, one of the first national anti-SDI petitions was circulated at Cornell University and was signed by two Nobel laureates and noted astronomer Carl Sagan. But the director of Cornell's engineering school has estimated that a quarter of the engineering professors have expressed interest in conducting SDI research.

One professor of electrical engineering, Lester F. Eastman, said SDI money could allow the continuation of his 10-year research into high frequency transistors. "Ours is all open research," Eastman said. "SDI is simply one more source of funding." On behalf of a consortium of scientists, Eastman has submitted a preliminary research proposal.

This unusual faculty debate has forced university administrators to play a delicate balancing role, weighing concerns of academic freedom against worries about becoming too involved with a politically divisive weapons system that ultimately may be deemed classified.

Some schools, like Michigan and Cornell, have issued statements repeating their long-standing opposition to classified research on campus but upheld the right of individual faculty members to conduct SDI research if they wish.

The question of whether SDI research will become classified has fueled faculty protests across the country. That central issue -- more than the added questions about the feasibility of the system -- has prompted Pentagon officials to seek to reassure university administrators in a series of private meetings and public forums.

A few schools maintain deliberate policies allowing -- even encouraging -- classified research on their campuses.

Those schools have been the beneficiaries of considerable SDI funding.

Georgia Tech, for example, which has no prohibitions against classified research, has received eight SDI contracts totaling $35 million over a five-year period, according to Thomas E. Stelson, the school's vice president for research. SDI contracts account for 7 percent of Georgia Tech's research budget.

Stelson said each of the projects funded by SDI money was begun long before Reagan proposed the project. "They are good, solid research programs that we've been seeking funding for for some time," he said.

Stelson said Georgia Tech scientists have been conducting classified research for over a decade, which has made that school's research program one of the fastest growing in the country.

"Our scientists take positions on all sorts of social issues," he said. "But one of the things I think they would find really objectionable would be for one scientist to tell another what kind of research to conduct.

"Many people think it's a raging controversy on campus -- but it's not here," Stelson said.