Constrained or Dependent Relative Motion

In some situations, the motion of a particle may be dependent on the motion of other particles. Generally, the particles are physically connected in some manner but not necessarily so.

An easy way to demonstrate this concept is to use examples involving particles connected by "inelastic" cords and pulleys. It is these connections that provide the constraint equations necessary to relate the motion of one particle relative to another.

See this example, which carefully derives the constraint equation for two particles connected by a system of pulleys and ropes.

Now that we have done a careful derivation, we should be able to more quickly derive constraint equations, e.g.

where

Notice that the particles do not necessarily have to move along the same line for the constraint equations to be valid.