Competing at the Olympics has earned fame for many. For many others, fame has followed a sporting career. (Hello Tarzan – or should we call you Johnny Weissmuller?) It is unusual, however, to find those who are already famous in other fields taking part in the Olympics.

"Who can he be thinking of?" I hear you ask in an ironic tone. Well, as of a month ago, I could have been thinking of Sir Paul McCartney's second wife, Heather Mills, who appeared set to ski for Britain's Paralympic team at the forthcoming Sochi Winter Games until an altercation with officials at an Austrian hotel over the ratification of a new prosthetic limb left her, as it were, out in the cold.

Mills now faces a fine of up to €1,000 (£817/$1,354) for allegedly verbally abusing and physically harassing the head of the International Paralympic Committee's Skiing Committee, Sylvana Mestre. I'm thinking the fine wouldn't be too much of a problem for her, but missing out on the Games following her World Cup silver in the adaptive slalom last year – she has now missed all relevant deadlines - surely will be.

Heather Mills looked on course for a Sochi 2014 appearance after taking World Cup silver in the adaptive slalom event in New Zealand last August. But her bid slid right off course after an almighty row ©Getty Images

On reflection, Mills's former husband qualifies in his own right, having played at the London 2012 Opening Ceremony after making a bit of a name for himself in a musical career.

But no. I am thinking of Vanessa Mae, the violinist who has sold more than 10 million albums worldwide, and who is now adding another string to her... er...violin after being selected to ski for Thailand in Sochi.

This is a truly inspirational outcome for the 35-year-old who took up skiing at the age of four, four years before acquiring the nickname "Teeny Paganini" when she became the youngest pupil at the Central Conservatory of Music in Beijing.

Under current Olympic qualification rules, countries with no skier ranked in the world's top 500 may send one man and one woman to the Games, to compete in slalom and giant slalom, and Mae, who has been training to this end since 2010, has done enough in qualifying to pass muster.

World renowned violinist Vanessa Mae is due to realise a childhood ambition having qualified to ski for Thailand at the forthcoming Sochi Winter Olympics ©AFP/Getty Images

She will be only the second Thai athlete to compete at a winter Games, where she will use her Thai father's surname of Vanakorn. "I am taking a plunge," she said four years ago. "It has been my dream, and I am hoping people will accept I just want to give it my best."

Having taken the plunge, she does not flatter herself that she will be making a big splash. She just wants to compete to her best ability - an attitude that the founder of the modern Games, Baron Pierre De Coubertin, would have readily embraced.

Sir Paul McCartney performs at the Opening Ceremony of the London 2012 Games. He had previously made something of a name for himself in the world of music ©AFP/Getty Images

Mae is not exactly a one-off, but she is in rare company. There is a relatively rich seam of those who have arrived at a Games with names already established - a royal seam.

At the inaugural modern Olympics at Athens in 1896, two Greek princes accompanied the Greek winner of the marathon into the stadium. Thirty two years later another royal personage - Crown Prince Olav of Norway, later King Olav V, became the regal deal as he won a gold medal at the 1928 Amsterdam Olympics as a member of the winning crew in the 6m sailing class.

Olav's son, Prince Harald, later King Harald V, also competed in Olympic sailing from 1964-1972. In 1960 another royal figure won an Olympic sailing gold in the Dragon class – Prince Constantine of Greece. His brother-in-law, Juan Carlos of Spain, took part in the 1972 Olympic sailing competition.

British subjects, among others, will recall Princess Anne's involvement in the three-day equestrian event at the 1976 Montreal Games, where she became the first member of the British Royal Family to compete at the Olympics, finishing 26th after recovering from a cringe-making fall during the cross country element. She confessed years afterwards that she had no memory not just of that fall, but of the whole of the second day's event. Give that girl a medal!

Princess Anne en route to winning the European eventing title at Burghley in 1971, five years before she made an Olympic appearance in Montreal ©Allsport Hulton Archive/Getty Images

Her husband-to-be, Mark Phillips, had been one of the team gold medallists in the three-day event at the previous Olympics, and at the London 2012 Games, of course, their daughter Zara Phillips was one of the home team silver medallists in the eventing.

There has been royal involvement in the Winter Games too, through Prince Albert of Monaco, who competed, as Albert Grimaldi, in the two and four-man bobsleigh from 1988 to 2002.

While Mae's switch from music to sport is unusual, there have been others who have arrived at the Games having made names for themselves in other sports. One of the first was Britain's Lottie Dod, silver medallist in the archery at the 1908 London Games having already won the Wimbledon singles title five times and the British Ladies golf championship once, not to mention having represented England at hockey.

Dod might also have excelled in a winter Games, had one existed in those days, as she also excelled at skating and tobogganing.

Then again, Mae might have had a cracking chance of Olympic gold had the Olympic artistic competitions, which included music, not been dropped from the main body of the Games after the 1948 version in London.

Spot the future winner of the 1912 Olympic literary gold medal - yes, it's Baron Pierre de Coubertin, seated left with fellow IOC members in 1896 ©Hulton Archive/Getty Images

Perhaps we might also add to our list the great Baron De Coubertin himself, who entered the 1912 Olympic art competition with a literary effort entitled "Winning isn't everything, it's the only thing" - only joking, it was called "Ode to Sport". Now the good Baron entered under a pseudonym - "Georges Hohrod and Martin Eschbach" – but, guess what? He won the gold medal. Do you think anyone might have suspected?...

Mike Rowbottom, one of Britain's most talented sportswriters, covered the London 2012 Olympics and Paralympics as chief feature writer for insidethegames, having covered the previous five summer Games, and four winter Games, for The Independent. He has worked for the Daily Mail, The Times, The Observer, The Sunday Correspondent and The Guardian. His latest book Foul Play – the Dark Arts of Cheating in Sport (Bloomsbury £12.99) is available at the insidethegames.biz shop.