Rheonomous
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A mechanical system is rheonomous if its equations of constraints contain the time as an explicit variable. Such constraints are called rheonomic constraints. The opposite of rheonomous scleronomous.
A mechanical system is rheonomous if its equations of constraints contain the time as an explicit variable. Such constraints are called rheonomic constraints. The opposite of rheonomous scleronomous.
Example: simple 2D pendulum
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 \sqrt{x^2+y^2} - L=0\,\! , where (x,\ y)\,\! is the position of the weight and L\,\! the length of the string. The situation changes if the pivot point is moving, e.g. undergoing a simple harmonic motion x_t=x_0\cos\omega t\,\! , where x_0\,\! is the amplitude, \omega\,\! the angular frequency, and t\,\! time. 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 \sqrt{(x - x_0\cos\omega t)^2+y^2} - L=0\,\! .
See also
Lagrangian mechanics Holonomic constraints
References
Text derived from https://en.wikipedia.org/w/index.php?oldid=1359365517 under CC BY-SA 4.0; modifications have been made.