ABSTRACT
We recall the variable t doesn't always explicitly appear in the kinetic energy T and potential energy V.
Remark. A rheonomic system can present a Lagrangian which is not explicitly dependent on time.
Indeed, consider a pearl following a circle c(o;R). If this last rotates about a vertical axis with a constant angular velocity m, then this example illustrates this remark. The generalized coordinate is the angle () (in the plane of the circle) locating the pearl from the horizontal plane ofequation x 3 =0 . The position of the circle is located by the angle co t in the horizontal plane and so, is explicitly dependent on time. The components of the position vector of the pearl in R 3 are
Xl = Rcos() coscot x 2 = Rcos()sinmt x3 = Rsin(). The Lagrangian
L = m (R2iJ2 + R2co2cos2 () - mgR sin () 2
is not explicitly dependent on t .
