In Taylor's advanced text on classical mechanics, he gives an example of a non-holonomic system, I find this part very strange.
He gives the example of a hard rubber ball being rolled in a triangle on a flat surface, the point is that if you take the ball out through the triangle and back to the initial position, the orientation of the ball will be different at the end.
I don't understand why that would make the system holonomic, if we treat the ball as a rigid body it would have 6 degrees of freedom, three numbers to specify its spatial position and three numbers to specify its orientation, it seems to me that only when we ignore the extended nature of the ball does the system become non-holonomic.
He gives the example of a hard rubber ball being rolled in a triangle on a flat surface, the point is that if you take the ball out through the triangle and back to the initial position, the orientation of the ball will be different at the end.
I don't understand why that would make the system holonomic, if we treat the ball as a rigid body it would have 6 degrees of freedom, three numbers to specify its spatial position and three numbers to specify its orientation, it seems to me that only when we ignore the extended nature of the ball does the system become non-holonomic.