General equation of motion of a machine
General mechanical engineering - Dynamics: machine theory

A machine is generally a one-degree-of-freedom system, i.e. the motion and mechanical actions involved can be expressed in terms of a single parameter, its first and second derivatives, and time.

We'll show that the equation of motion takes a unique form. Lagrange's method (see article of this treaty) is well suited to achieving this result.

• General form of kinetic energy

  Since the system has a parameter q, for any point P, we formally have : $\begin{array}{c}\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{OP}}\left(q\right)\\ \end{array}$