You're taking the dot product of the start vector ...

2007-08-27T15:36:00.000-07:00

You're taking the dot product of the start vector and the current vector, and assigning it directly to angle. Shouldn't angle get the inverse cosine of the dot product instead? Dot product returns the cosine of the angle between vectors, not the angle.

Comments on Nostatic Software Dev Blog: A TV3D ArcBall implementation

You're taking the dot product of the start vector ...