I'm curious to know if, in most professional orchestras, a principal player will double another instrument if called to do so. In particular, will (a) the principal flute ever double piccolo or alto flute, (b) the principal oboe double English Horn or oboe d'amoure, (c) the principal clarinet double bass clarinet or e-flat clarinet, or (d) the principal bassoon ever double contrabassoon. For example, in Dvorak's 8th, the principal oboe is directed to play English Horn for a rather short passage in the first movement. In practice, will the player perform that passage or defer to the 3rd Oboe/English horn player (who incidentally wouldn't have anything else to play except that passage)? In Kodaly's Hary Janos, all four flute players are directed to play piccolo for a trill in the "Battle with Napolean" section. Will the principal player play piccolo or will additional players perform the passage instead? I don't think I've ever heard of a principal bassoon being directed to play contra, or for a principal clarinet to play anything other than the usual B-flat/A clarinet pair. Thanks!
It's pretty much up to the orchestra's managing group. Assuming that the 'extra' instrument is playing only when the 'main' instrument is not, there's no reason the principal or second player couldn't double.
Union rules may apply in some areas :-) . In practice, some instruments are pretty much left to specialists. This usually includes the lower family members such as bass clarinet, contrabassoon, maybe a couple saxophones in 20th-cent compositions. The soprano/sopranino instruments such as piccolo and Eb clarinet tend to be played by the "regulars" in my experience.
Moving to the brass section: I'm not aware of any, say, trombonists doubling on euphonium or tuba, but trumpets almost certainly would pick up the rare cornet or flugelhorn part.
Percussionists, of course, play everything they can hit with a stick :-)
Usually the principal players don't switch if they don't have to. Suppose there are two flutists and at some point the score calls for one piccolo; the second flutist will double. On the other hand, if the score calls for two piccolos (or if there is only one flutist in the first place) the principal would have to switch instruments, since an extra person on stage is mighty expensive. (And at least where I live, classical music gets both less and less government funding and smaller and smaller audiences. Professional orchestras are disappearing and shrinking.)
Of course, if the score calls for these "extra" instruments in addition to the normal woodwinds, additional musicians would be needed.