Читать книгу Introduction to Mechanical Vibrations - Ronald J. Anderson - Страница 18

The generalized coordinates are simply the degrees of freedom of the system with the condition that they be independently variable. That is, given a system with generalized coordinates (), any generalized coordinate, , must be able to undergo an arbitrary small variation, , with all of the other generalized coordinates being held constant.

In the example just considered, we might try to specify the position of the bead on the wire by using two coordinates – the vertical distance from and the horizontal distance from . We would soon find that these coordinates are not independent because the bead is constrained to stay on the circular wire so changing the horizontal position requires a change in the vertical position. These two coordinates are therefore not generalized coordinates.