Next Wednesday night, the little people of Utah and their parents, uncles, aunts and cousins will begin their annual trek to Ballet West's "Nutcracker."

And before the curtain rings down on the last of 21 performances, 35,000 or more patrons will have seen Willam Christensen's popular setting of the Tchaikovsky classic in the Capitol Theater.The schedule calls for 7 p.m. performances on Dec. 14-17, 19-23 and 26-28, with 2 p.m. matinees on Dec. 17-18, 21-23 and 26-28, and a noon matinee on Christmas Eve. Tickets are now on sale at the Ballet West box office in the theater, 50 W. Second South, or at Smith'sTix. For charge sales, call 533-5555, or 800-888-8849. Prices range from $7-$20, with discounts for groups of 20 or more and for senior citizens. Some performances are already sold out.

"Our first `Nutcracker' in 1955 was immediately a big success," said Christensen. "A few years later, a friend asked me, how long can this `Nutcracker' keep running, Bill?' I answered, `How long will Christmas last?' "

Now in its 34th Utah incarnation, the Christensen "Nutcracker" shows no signs of aging, or losing its popularity. Christensen's was the first in America (in 1944, in San Francisco), and most Utahns would tell you it's still among the best, though "Nutcrackers" are now scattered broadcast across the land. Actually, Mr. C's version figures prominently in the new "Nutcracker" at San Francisco Ballet, where artistic director Helgi Thomasson relied heavily upon his counsel and experience in re-staging.

" `Nutcracker' is an American phenomenon," said Christensen. "It's nowhere nearly so popular in Europe, and certainly not in Russia, where it all began. I feel our success is because we use the children, and we have not been afraid to revise and experiment."

Ballet West does use children in abundance _ 260 of them in four casts, gleaned from 800 hope-fuls. (Two more casts were assembled in Spokane and San Antonio for tour dates.) This includes several each of Claras and Fritzes, Drosselmeyer's nephews, buffoons, soldiers, toys, pages, Oriental servants, mice and party children.

Magic takes over for them and their elders, at the party in the Stahlbaum's cosy parlor in Nur-emburg, when Herr Drosselmeyer gives Clara her beloved Nutcracker. Magic continues in the midnight fight between mice and soldiers, and magic reigns supreme in Clara's fabulous journey, on the arm of her prince, through the Snow Kingdom to the realm of the Sugar Plum Fairy.

Perhaps the perennial success of Christensen's "Nutcracker" rests upon the heart-lifting resolves that underpin this ballet: "Let's give a party," (Act I) and "Let's give a show" (Act II).

Marius Petipa, genius of the Russian ballet during the last half of the 19th century, well understood the appeal of these suggestions. Born in Marseilles to a balletic family, Petipa was an excellent danseur in his youth. When he gravitated to Russia, it was for keeps.

Russian by temperament, a born manager and prolific choreographer, Petipa led the St. Petersburg Imperial Ballet (now the Kirov) at the fabled Maryinsky Theater through a golden era, from 1869 to 1903. There, in more than 60 ballets, he maintained artistic integrity with a minimum of vulgarity, while catering to the often frivolous tastes of the royal court.

For them he developed not so much a formula, but a pattern of interpolating a divertissement, or series of dances called entrees, to show off individual dancers _ a sort of dance revue, if you will. The divertissement usually came at a special celebration: for example, in "Sleeping Beauty," the fairy tale characters who dance at "Aurora's Wedding" (sometimes performed separately), or the Prince's coming-of-age ball in "Swan Lake," with its elegant regional folk dances.

For Tchaikovsky's third ballet, "The Nutcracker," (1892) Petipa had already worked out his scenario, with detailed instructions to the composer. However, being human and fallible, he fell ill and had to turn the task of choreography over to his ballet master, Lev Ivanov. Ivanov (choreographer of the sensitive "white" acts in "Swan Lake") created a "Nutcracker" reportedly of great charisma.

A talented premier danseur who contented himself with character roles, a phenomenal musician-composer who could play a ballet from memory at the piano after one or two hearings, yet refused to study music seriously, Ivanov was somewhat of an enigma. He has been called a sort of Chekovian character, "a man of subtle, easily wounded nature, kind and benevolent, ready to sacrifice himself for the benefit of egoistic careerists."

Perceiving in "The Nutcracker" a great opportunity, Ivanov choreographed from the heart. His was a totally musical-emotional interpretation, stressing Clara's development from a little girl playing with dolls to the dawn of love, through dreams of a brave and manly hero.

His choreography for "Waltz of the Snowflakes," was a symphonic masterpiece, a 19th century Busby Berkeley extravaganza for 60 corps dancers and eight soloists. Reportedly they created the illusion of falling snow, as the dancers formed a star, then assembled into a huge snowball, and finally a bank of snow. According to Vaganova, connoisseurs bought seats in the upper tier to admire the beautiful patterns of the dance.

Christensen's "Nutcracker" was rooted in the memories of Alexandra Danilova and George Balanchine. Both were trained at the Maryinsky Theater before the Revolution, and while on tour in San Francisco they spent one fateful evening with Christensen, dredging up their childhood memories of the Ivanov choreography, which formed the basis of Christensen's interpretation.

The divertissement prescribed by Petipa gave Ivanov the most trouble _ to his mind, an intrusion upon his ideal of the plot's musical and emotional flow.

Ivanov to the contrary, the "Nutcracker" divertissement has triumphed in America, and the elaborate program that honors Clara in the land of the Sugar Plum Fairy has as many variations as there are companies dancing it. Most pay a kind of obeisance to the originally-prescribed parade of nations. For example, Christensen highlights Arabian, Chinese, Russian and French flavors, capped by Mother Buffoon, a character seemingly plucked out of Punch and Judy.

And it is the opportunities of the divertissement that fire up the corps of Ballet West, according to Sondra Sugai. Now assistant to the artistic director, Sugai has been involved with "The Nutcracker" since 1965 _ as dancer, regisseur, and audi-tioner and coach of children's casts. Indeed, she met her husband, Christopher Fair, when both danced the Chinese variation.

"With such a concentration of performances, often two a day for several days, we are cast four and five deep on most roles," she said. "The variations and small dances of the first act, and the big production numbers like the Snow and Waltz of the Flowers give our corps dancers a chance to move out into solo parts and be noticed."

More than one principal dancer of Ballet West has first showed her stuff in mini-principal roles like the dancing doll or Arabian enchantress, or perhaps as a trickle-down replacement for the Sugar Plum Fairy. And while they are not part of the divertissement proper, children dancing the pages and Oriental servants are grateful for the restoration of their short dances. Terence Kern will conduct the dancers and Utah Symphony. On Wednesday afternoon, Ballet West will give a special performance for handicapped and disabled children, thanks to a grant from the Salt Lake City Arts Council. The popular Sugar Plum parties, at which children may go onstage and visit with performers, will be held following the matinees of Dec. 23, and 26-28. Tickets are $5.