Amechanical systemisrheonomous if its equations of constraints contain the time as an explicit variable.[1][2] Such constraints are called rheonomic constraints. The opposite of rheonomous is scleronomous.[1][2]
As shown at right, a simple pendulum is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length. Therefore, this system is scleronomous; it obeys the scleronomic constraint
,
where 
The situation changes if the pivot point is moving, e.g. undergoing a simple harmonic motion
,
where 
Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore, this system is rheonomous; it obeys the rheonomic constraint
.Constraints are further classified according as the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous).
In many mechanical systems of importance the time t does not enter explicitly in the equations (2) or (3). Such systems are sometimes called scleronomic. In others, as for example those involving moving constraints, the time t does enter explicitly. Such systems are called rheonomic.
