ANALYTICAL MECHANICS

Аннотация

The difference between the two types of constraints is very important for the physics. We have already seen that it is necessary to find not only but also if the constraints introduce a q dependence into the kinetic energy. For example, one could have a particle constrained to slide on the surface of a sphere. This has two degrees of freedom, since the distance r of the particle from the center of the sphere is constrained to be the radius of the sphere R. But suppose the radius of this sphere is changing in a predetermined way with time: R = R(1). You would expect to get a completely different answer for the motion of the particle in this situation.