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You would think that a sexually polymorphous musical that combines a Renaissance pastoral romance with the songs of the 1980s California rock group the Go-Go’s would at the very least be a hoot, a show that could get sloppy drunk on its own outrageousness. Yet “Head Over Heels,” which opened on Thursday night at the Hudson Theater, feels as timid and awkward as the new kid on the first day of school.

Make that the new kid who longs to run with the wild crowd but can’t quite commit to being as bad as coolness demands. Directed by Michael Mayer, who has been more than competent at the helm of Broadway rock musicals like “American Idiot” and “Hedwig and the Angry Inch,” “Head Over Heels” lacks the courage of its contradictions. It mutters deferentially when what you want is a rebel yell.

Paradox is at the heart of this production, which was conceived and originally written by Jeff Whitty (“Avenue Q”), then adapted by James Magruder (best known for his stage versions of literary classics). It was Mr. Whitty who had the idea of reimagining Philip Sidney’s “The Arcadia,” a 16th-century fantasy of trouble in paradise, as a picturesque frame for the pop hits of the Go-Go’s.

That all-female band, as you may know (and if you don’t, you are not this production’s target audience), rode its rough-edged combination of punk riotousness and surfer-girl sunniness to the top of the pop charts in the early 1980s. Though many of their hits ponder the vagaries of love, they otherwise have little in common with an arcane literary universe that is usually the province of graduate students.