PUKSY Rostropovich dashes onstage and barks at the National Symphony, which is creating a din with cymbals crashing, tympani tuning and a hundred instrumentalists practicing. As her master starts rehearsal, Puksy settles down at his feet to sleep.

Nearly every minute Mstislav Rostropovich stops the orchestra with corrections. Forty minutes into rehearsal the music on the stands is still opened to page one. An hour into rehearsal, he wants to begin again at the beginning.

"LA, BAH, BAH!" he shouts, shaking his fist and stamping his foot to emphasize the beat.

There is a shrill cry.

The music stops. The musicians gasp and Rostropovich looks down as Puksy limps out from underfoot. "Ex-cuse me, " he says elaborately, bowing trom the waist, but she rushes off the podium.

Rostropovich lifts the baton and playing resumes, but he keeps calling softly to Pusky, who sulks beneath the concertmaster's chair.

When the movement ends, Rostropovich calls her again, more insistently. "Puksy! Come here. Come here. I said excuse me, Puksy!" Finally, she relents and he returns undivided attention to the rehearsal.

Rostropovich the cellist has long inspired hysterical adulation, and now that he is also a conductor, he seems to be even more popular. Since arriving in Washington last fall to take charge of the National Symphony Orchestra, he has been at the center of a storm of attention. Critics complain that Rostropovich the conductor sometimes take too much freedom with the music and point out that he heavily favors the Romantic repertoire. But no one debates the fire and imagination he brings to the podium or the sudden dramatic improvement in the orchestra. All his concerts in Washington have sold out. His performance with Isaac Stern of the Tchaikovsky Violin Concerto was being pronounced "the recording of the decade if not of the century," even before it had been taped. His appearance is requested wverywhere, here and abroad, and interviews are sought by the press from around the world.

Naturally, the object of these attentions is not displeased, particularly because it is rather different from what he had become accustomed to at home in the Soviet Union. For his vociferous public protests against governmental abuse of Aleksandr Solzhenitsyn, Rostropovich and his wife Galina Vishnevskaya, who was the prima donna of the Bolshoi Opera, had become non-entities.

At first they were prohibited from performing abroad; then appearances were barred at home. Eventually, no mention of their names was allowed anywhere: their careers were at a dead end. Through Senator Edward Kennedy, who spoke personally to Soviet Premier Leonid Brezhnev on a visit to the Soviet Union, Rostropovich, his wife and two daughters obtained passports. They left Russia in 1974.

"Very different here," Rostropovich comments when we first meet. "Everyone shows me the reviews and stories. I am very grateful so much paper is used up for me."

His office at the Kennedy Center is a small windowless room behind a plain white door. It is dim but cheerful inside - the room in informal disarray, the aroma of coffee brewing in an electric percolatoA brown paper carton, not yet unpacked, occupies the center of the room. On one side there is a piano, to the other shelves holding an immense Hitachi stereo system, a few books and recordings, a pre-tied black evening tie, a can of Sure deodorant. The walls are bare except for a somber photograph of Shostakovich, his mentor and longtime friend, and a wood and gilt icon of St. Nicholas the Miracle-Worker.

Rostropovich slouches in a deep arm chair at the far end of the room, one arm around Puksy, who is cuddled up like a baby at his shoulder. His dress is insouciant: dark wool slacks and a wrinkled peasant overshirt of unbleached muslin. He is larger in both directions than pictures sugges and there is a distinctly sly cast to his expression.

An interpreter sits at the ready, but he speaks in English, consulting her only occasionally. Hearing my proposal to spend a day in his life from morning till night, he expansively suggests a week instead. We compromise at two days.

Rostropovich's charm is, of course, legendary. But the surprising thinkg about it is that literally everyone - from busboys to prima donnas, poets, doormen, secretaries, even other musicians - seems to be equally susceptible to "Slava," the nickname used by almost everyone who knows him.

Rostropovich professes no interest in the subject and explains it much the way he once explained what makes him the world's greatest cellist: "I don't even know why my hands do certain things sometimes. They just grab for the notes."

He is much more interested in speaking of Russia, and of how musicians are totally controlled from "above." Criticism and reviews are always turned in a certain direction and contain "opinions" from the highest levels. He describes the case of the respected conductor of the Leningrad Philharmonic, Genadii Rozhdestvensky. Through a review there came an official "opinion" that he should be removed from the orchestra.

"A new conductor was appointed who, until that point, had almost never conducted a symphony. He had been conductor of" - Rostropovich collects himself before uttering the scandalous words - "balalaika orchestras." There were protests but they did no good, and "regardless of the quality of the performance, the reviews were always brilliant."

To be sure, Rostropovich is aware that he has had "official help from the top." For instance, the opportunity to debut abroad, which Rostropovich had when he was 20, in 1947. Not everyone is sent abroad, and it is a critical question, Rostropovich explains, quoting from Pushkin: "Russians are predisposed to believe all Western opinions."

There is also the question of reviews. The Soviet papers will excerpt from concert reviews in Western papers, and whether they excerpt favorable or unfavorable comments or are silent altogether is most significant. "If nothing is printed, people assume he didn't do well. But if they see rave reviews, they think, Ahhh. " His eyes widen in mock wonder.

"My life is full with problems," he says, suddenly back in the present, and begins to enumerate: the orchestra repertoire must be widened, which means commissioning new works; programs for next season must be planned, guest soloists and conductors engaged; and there is the work of improving the orchestra itself. "The beginning of anything is very difficult," he says, ever the diplomat, "and the beginning with the orchestra was also very difficult."

Symphony manager Robert Noerr arrives and Rostropovich kisses him three times and asks for the exact time: 9:56:45. He consults a second opinion before making an adjustment on his watch. Rehearsal is scheduled for 10 a.m. and he doesn't want to miss a second.

Rehearsals are strictly regulated by contract and every minute of overtime is costly. But even with a lot of overtime, there is still not enough time to prepare. The program at hand is difficult, with two works by Schulmann and Prokofiev's massive "Alexander Nevsky" Cantata, which has not been performed by the orchestra before.

In rehearsal, Rostropovich remains calm. There is not a hint of intimidation in his manner. Asked about this later, he said, "If it's clear what I want, why must I act in a tough manner? I'm sure that if you ask someone to do something, they will do more than if you just order them to do something." Another time he put it differently: "I'm a human being and I understand it's difficult for each musician - we have enough troubles in our lives. That's why I ask 'Please play,' not 'You must play.'"

But always he wants more: more precision, more expression, more contrast. "Vibr-rato! Vibr-rato!" he calls to the violins, his hand a blur of motion, as they rehearse Schumann's lush, romantic "Second Symphony." Some of the violinists are making nearly imperceptible vibrato.

A moment later, his hand is pressed to his heart. "Shh. Shh. Very intime. " He throws them a broken-hearted look.

After rehearsing a phrase repeatedly, he raps his baton on the music stand. "We have a very short time to make this perfect." He corrects himself: "Not perfect, but better." It is as close as he comes to anger.

During the break, Rostropovich is surrounded by musicians with questions, and he is followed offstage by an older violinist. "I know you look out on a sea of violins," he is saying, "but I must know. Is my playing too passionate, too intense?" "You are very passionate and intense," Rostropovich replies, not quite understanding. "But are you satisfied?" the musician says, as if he is about to cry. Finally Rostropovich puts an arm around him and says, "I'm satisfied."

Rostropovich likes to speak of the orchestra as his "family," but since his arrival it has been a family with a lot of tension. He announced that he would keep all the players for the first season and then take a hard look. Several musicians have already been dismissed.

For "Alexander Nevsky" the stage is crammed with full orchestra and a chorus of more than 100. It is a very dramatic, very Russian piece of music which tells the story of the unification of the country during the Middle Ages. Rostropovich is openly concerned. Great performances, after all, are usually achieved after a conductor and orchestra have worked together a long time - years, not weeks.

Right from the first of its seven sections, "Russia Under the Mongolian Yoke," there is trouble. It takes precious minutes to get a certain effect from the brass. "Make it like heavy breathing," Rostropovich suggests.They simply play louder. Eventually he says: "Make it like a snore. Inhale . . . exhale . . . SNORE . . . SNORE."

They try again, unleashing tremendous porcine snorts. The effect is sensational.

At one point he suggests to the woodwinds: "Play as if you are being tickled in the sides, ah-hahaha, ah-hahaha."

To the chorus at the finale: "You sing nicely, but I want you to sing like fanatics."

Rehearsal runs an hour and a half overtime. Although the musicians have the right to leave when overtime is called, no one does.

Returning to Rostropovich's office after rehearsal, I was met by the interpreter with pusszling news: private meetings - which I later learned concerned the delicate matter of firing the first flutist, a long-time member of the orchestra who was no longer playing very well.

The following day Rostropovich was again "busy." Further, the interpreter thought it unlikely that he would have any more time that week or in the future for interviews. I was dismayed, but there was nothing to do but observe him in action for the next several weeks.

Besides attending endless receptions, teas, parties and other ceremonial occasions - which Rostropovich does partly for the benefit of the orchestra, partly because he enjoys it, and partly because he can't say no - his responsibilities as musical director of the orchestra extend far beyond conducting three concerts a week for twelve weeks a year. He rehearses the orchestra five mornings a week, holds sectional five rehearsals, tours with the orchestra and conducts recording sessions. He is especially interested in finding outstanding but unknown young musicians to perform with the orchestra, and has arranged a nationwide competition to select young singers for a concert next season.

He handles personnel problems ranging from the players' financial conditions to their health. He recently negotiated a better recording contract for the orchestra and even edited a press release for an upcoming concert. No detail is too small: he concerns himself with everything.

His greatest task, of course, is to improve the orchestra. The Symphoby made a large financial commitment toward this end by hiring Rostropovich in the first place - at a salary reported to be more than $100,000 a year. But the Rostropovich magic alone will not be enough. Funds have been provided to add ten violinists to the orchestra, bringing the number up to that of the top orchestras, at a minimum cost of $200,000 per year.

It is Rostropovich's job to fill these openings, and national auditions are scheduled for this month. If players or real quality are found, it will immediately make a major difference. However, Rostropovich does not intend to settle for the ten best among those who apply: "If not good enough, I only take two."

Compounding Rostropovich's difficulties is his full schedule of cello concerts. Immediately after conducting his fall series of National Symphony concerts, he departed on a heavily booked tour and returned to Washington just before his second six-week series began on January 10.

Somehow, time was made - a cancelled appointment - and there he was, patting the seat right next to him on the sofa and saying, "I've missed you." It was said in such a way that I felt the edge going out of my resentments and suspicion. Pusky licked my hand profusely and curled up in my lap.

I was curious about why he works so hard. He sipped his tea and said, "Very difficult answer." To begin with, the repertoire for cello is very limited: "For cello, only a few great works, Schumann, Dvorak, of the highest quality . . ." he trailed off. "But with the orchestra I work with music of incredibly high quality . . . I have possibility to conduct all Beethoven!" There is also the satisfaction of recording. It's an unimaginable pleasure, he said, to record a composition with the orchestra and "then to hear your own interpretation into which you've poured all your soul, heart and knowledge . . . for this satisfaction it is worthwhile."

At the same time he feels compelled to keep up his cello playing as before - for himself and for others.

He was tired and his English was less precise: "For Columbia (his concert agent), for my friends who love my cello playing, it not matter that I have commitments to conduct the orchestra, to make record with my wife, to conduct in Europe. These people need from me my cello playing - also myself. So I must make not too much less than before." He must cut down, he added, but not so it is noticeable.

Then he spoke in Russian. "Maestro says," the translator reported, "that he intends to work as hard as he does now until he is dead. Further: if people suffer a great deal from Slava's music, then he must warn them that their suffering will end only when he dies."

Still, I pointed out that he had done nothing to make his new job any easier, and it seemed as if he'd tried to do the opposite, by scheduling several world premieres at the beginning of his first season, plus many other works that were new to the orchestra.

He shrugged. "It depends what you live for. We exist in order to better ourselves each day." Of course. He is a perfectionist and his moments of self-satisfaction are fleeting.

"For today - yes, that's a good performance," he admitted. "Next day, next concert - a litter better."

He did allow that he is pleased with the progress of the orchestra so far and feels that they are playing "obviously more finely." He is getting the response from the orchestra that he wants and hopes to develop it to a higher level. "Not perfect yet," he summed up the orchestra after the first six weeks, "but much better."

Suddenly there was a torrent of Russian words. Rostropovich was speaking to the translator and pointing to Puksy who had been asleep in my lap for the past hour. He beckoned her in Russian and she woke up but didn't budge. He insisted. She taunted him by climbing into the translator's lap. Only when he seemed completely beside himself did she obey. I suggested that she was only trying to make him jealous. He laughed politely but didn't sound amused.

Typically, one of the answers I had been pursuing for weeks came quite unexpectedly when I asked about the sources of his genius. He is the son of a cellist and a pianist but there is nothing in his background to suggest that he would be extraordinary. He was stern: "There is no genius. Absolutely not." Then he was off again in Russian.

"Slava has only incredible love for music. He will debate anyone on his point. He knows his love for music is greater than anyone else's on earth. This can be a funny situation. He can start crying without any reason. He hears the most beautiful sounds in his head . . ."

"I try to recreate this ideal," he broke in. "When I make music I try to imitate that sound. My cello playing has been recognized as pretty good . . ."

There was an objection from the translator to these last words, but he repeated: "Pretty good." Then he was silent for a long minute before finishing his thought: "But with my playing, I come only halfway to my ideal."

Always there is music in his head, and it is usually accompanied by thoughts of how to reproduce it. At the moment he was hearing the beginning to "Walk to the Paradise Garden" by Delius and thinking about how there must be no border between silence and the sound.

He was first aware of music in his head at the age of four, when he composed a polka. His father wrote it down. "It had nothing to do with a polka. It was awful." He relented: "For a four-and-a-half-year-old it would have been completely unbearable, but for a four-year-old, not too bad."

He was a sentimental, romantic boy, he said, because he couldn't listen to Tchaikovsky without crying. When his godmother heard him listening to music and crying, she would give him candy. "And I liked that, so I cried all the harder."

Rostropovich insists his new life in Washington isn't lonely, even though his daughters, a pianist and a cellist, are in New York at the Juilliard School and Galina Vishnevskaya has singing engagements far and wide and is seldom in Washington. He could be lonely, but he doesn't have the time. Anyway, he says, "I live only for music."

Not quite true. It may be a frame of mind necessary to paving the way home to Russia, where Rostropovich has said he hopes to go someday. But this is the same person who jeopardized his citizenship and his whole career - and those of his wife and daughters - for an ideal. He didn't stop at offering Solzhenitsyn refuge at his country house, but went so far as to write a public letter protesting treatment of Solzhenitsyn - and when the Soviet papers wouldn't publish it, he gave a copy to Western journalists.

As I said goodbye, Rostropovich hugged and kissed me warmly. And as I left, it occurred to me why he elicits the response in others that he does. You can sense that it sometimes gets lonely out there in the world of the Platonic ideal, and that he truly does need you, even if it is just for the moment.