On the generalized Euler equations

In this paper the Euler equations applied to the motion of bodies placed in the frames of reference subjected to acceleration are presented. Positions of bodies are defined with respect to these frames by n generalized coordinates. Therefore, it is possible to establish an equivalence between the generalized Euler equations, the generalized Kane's equations and the generalized Lagrange's equations valid for accelerated frame of reference. General formulae for the generalized inertial forces together with the way of their application to general cases are given. Application to a special case of a rigid body is added. This problem was considered by Lure [2] in a completely different way; however the physical interpretation given in this work allows us to formulate general and complete expressions for inertial and gyroscopic for ces and to establish the differences between them.