General mechanical engineering - Dynamics: study of states

The dynamic equations, obtained by Lagrange's method or by the general theorems without the dynamic unknowns, constitute a 2nd-order differential system. These equations can be reduced to first order, a result that can be obtained directly by Hamilton's method.

A known solution of this differential system is called a state of motion.

Solving differential equations is a difficult problem. Fortunately, there are two remarkable states of motion that are very common and relatively easy to study:

• At steady state;

• stationary state.

With the notion of states of equilibrium and states of motion goes the notion of stability of these states. This is also one of the fundamental problems of mechanics.

These results can be applied to a wide range of fields, including :

• celestial mechanics;

• control of dynamic systems ;

• aviation;

• astronautics;

• automotive ;

• rail vehicles ;

• engineering structures.

It should also be noted that the notion of equilibrium goes far beyond the realm of mechanics (biometrics, econometrics).