Scleronomous constraint

Remarks

Example: the pendulum constraint $\abs{x}^2 - \ell^2 = 0$, with fixed length $\ell > 0$, does not contain $t$, so it is scleronomous. Non-example: a bead moves on a wire ring of radius $1$, centred at the origin in a vertical plane through the $z$-axis. The ring turns about the $z$-axis with angular speed $\omega \ne 0$. The bead obeys $x \sin(\omega t) - y \cos(\omega t) = 0$ and $x^2 + y^2 + z^2 = 1$; the first equation contains $t$ explicitly, so it is not scleronomous. When all constraints are scleronomous, the positions of the particles can be written as functions $x = x(q)$ of generalized coordinates $q$ alone, without $t$.