Lawrence Hogan Jr., son of and aide to the departing Prince George's County executive, remembers stepping onto his office balcony during the height of a 1980 county workers' strike and being spotted by a picketing public works employe, who started yelling into his bullhorn.

"Jump!" the man shouted, soon leading a chorus of 200. "Jump, jump, jump!"

"Two hundred people are shouting for me to jump off the balcony," the younger Hogan said last week. It was, he added wryly, "the highlight of my career."

It also was a symbol of the tumult that often marked the four-year reign of his father, Prince George's Executive Lawrence J. Hogan, a Republican whose penchant for strong statements and tougher stands formed a style that his successor, Democrat Parris N. Glendening, has pledged to work hard to avoid. Glendening, 40, who will be sworn in as county executive today along with a new, nine-member council, campaigned on a promise to not only solve the government's problems, but to do so in a way that he said would "avoid the confrontational style . . . and will say to people, 'Let's rough this thing together.' "

In a county that has witnessed four years of shrinking resources fought over by a Republican executive and a contentious all-Democratic council, both the new executive and new members of the council promise sweeping changes, starting today. And they have pledged to make those changes together.

Glendening, an ambitious political science professor with a fondness for quoting Winston Churchill, has promised that his administration will be "one of the best-planned, most goal-oriented the county's ever seen."

He says that he will provide leadership, backed by the meticulous preparation befitting a man who planned his executive campaign two years in advance and marks evenings with his family into his calendar each week.

The key to his success, he says, will be cooperation with the County Council, state legislature and various interest groups.

The County Council, meanwhile, is the first to be elected entirely from single-member districts and the first in a decade in which a majority did not run together on a single slate. Many of these council members won their primaries by narrow margins. Thus, for political as well as personal reasons, they are expected to place a greater emphasis than their predecessors on constituent service and district concerns, allowing Glendening to fulfill his desire to be the leading voice on county issues.

"Writing all the bills is fine, but I enjoy the constituent service, being able to do the little things . . . that really mean a lot to that individual," says Councilman-elect Anthony Cicoria, a trophy salesman and former state delegate from Hyattsville whose attendance at meetings with district senior citizens was considered superior to his record of showing up for votes in Annapolis.

Two-term incumbent Frank Casula, 62, who is expected to be elected council chairman when the new government takes office tomorrow, also is a master of the constituent-service school of county politics. So is Sue V. Mills, the former antibusing activist who was elected to her second term this year. Casula's former aide James Herl, 29, newly elected to a College Park-based seat and the youngest member of the new council, wants to be one, too.

The other returning incumbents are Floyd Wilson, of Glenarden, and William Amonett, of Brandywine. Newcomers are Richard Castaldi, a former mayor of Greenbelt, Hilda Pemberton, a former personnel specialist from Landover, and JoAnn Bell of District Heights, a former school board member.

Many of the new members also have vowed to overturn the decisions of the old council majority. The new council, Cicoria said, "will not be in the hip pockets of the zoning attorneys. The direction of our county will be changed now. The people will have representatives."

Already Sue V. Mills, the previous council's perennial outsider and one of four incumbents to win reelection, has begun to try to persuade the newcomers to rescind the former council's decision to grant a tax break to the Washington Capitals hockey team, and to place the Green Line Metro terminus at Rosecroft Raceway. But the success of both those efforts was in doubt last week after Mills was rebuffed in her bid to be council chairman.

Of the major issues confronting the county in the next few years, the budget is the most pressing, Glendening and the council agree. Glendening has estimated that the county's budget will fall between $30 million and $40 million short of the revenue needed to maintain current services. Unless other sources of revenue are found this year, he said, the county might confront layoffs on a scale of the 507 teachers who were fired in last spring's budget crunch.

The problem is exacerbated both by the voters' rejection last month of a charter amendment that would have loosened the county's strict ceiling on property tax revenue, and the expiration next year of labor contracts with virtually every major public employes' union.

Although Hogan and some other officials have disputed the size of the shortfall, Glendening has seized the issue as a way of distancing himself from Hogan, who ran a losing bid for a U.S. Senate seat this year. While Hogan failed, according to Glendening, to alert the community to fiscal problems before they occurred, "we're not going to be caught off guard, whipsawing in the streets about the budget."

"I think it is essential to have positive, candid discussions about alternatives. We do not intend to have any surprises," Glendening said. "The major policy choice is: Do we increase revenue by finding a nonproperty tax source, or do we decrease services?"

To seek solutions, Glendening followed his academic instincts and formed eight citizens' task forces soon after the election, each with an area of study. He gave one of them the task of studying the county's fiscal picture. Those groups are expected to deliver their reports to him on Tuesday. Glendening also has attempted to apply the scholarly approach to his choice of appointments. He will, he declares, have only "qualified professionals" in top county jobs.

Where Glendening's intellectual ability may fail him is in his personal relations with the powerful and demanding state delegation. Many legislators resented his calling publicly for more state aid before he had consulted them, and they have appeared to resist his appeals for help.

"I think there's a perception that Parris has some very heavy IOUs to the unions, and I don't think the delegation is willing to impose new taxes solely to finance Parris' IOUs," state Del. Timothy F. Maloney said a week after Glendening's landslide victory. "But I wish Parris well, not for his sake, but for the county's."

Moreoever, Glendening's friends say privately that his almost effortless climb to the county executive's seat may not have adequately prepared him for the vicissitudes of the job.

"In terms of intellectual ability , Parris is well prepared for the job," said his friend and transition team chairman, Lance Billinsgley. "But in terms of having the political limelight focused on him, that is certainly going to be a new experience. I am concerned that his skin is perhaps going to have to get a little bit tougher."