| Contents |
|
In this paper one studies the
dynamical system of a rheonomic nonconservative mechanical system, whose evolution curves are given, on the phase
space $TM\times R$, by Lagrange equations of the form:
\[
\frac{d}{dt}\left( \frac{\partial L}{\partial y^{i}}\right) -\frac{\partial L
}{\partial x^{i}}=F_{i}(x,\dot{x},t);\,\,\,\,\,y^{i}=\frac{dx^{i}}{dt}=\dot{
x^{i}},
\]
where $L(x,\dot{x},t)$ is a regular rheonomic Lagrangian, $F_{i}(x,\dot{x},t)$
are the components of an external force defined as a $d-$covector field
on $TM\times R$.
One can associate to the considered mechanical system
a vector field $S$ on $TM\times R$, which is the canonical semispray. Then all the geometric objects of the rheonomic Lagrangian mechanical system will be derived from $S$. |
|