A rheonomic gauge theory

In the paper we shall consider the manifold E=RxTM fibred over RxM and we shall define the rheonomic gauge transformations, the rheonomic gauge non-linear connections and the rheonomic gauge M-linear connections. Next, we shall study the global and local invariance of rheonomic gauge Lagrangians generalizing the main results from [5] and [7]. Moreover, we shall study the rheonomic strength fields and Lagrangians for rheonomic gauge fields. In Lagrange manner we shall determine the equations of motion and conservation laws for the rheonomic full Lagrangians.