ABSTRACT

The concept of constraint plays an essential role in analytical mechanics. Both Newtonian and analytical mechanics work with notions like: material point (particle), velocity, acceleration, mass, force, kinetic energy, mechanical work, etc., but the notion of constraint is specific to analytical mechanics only. The difference comes from the acceptance of the concept of ”freedom”. In Newtonian mechanics, a body is free if no force acts on it. For instance, consider a body under the influence of gravitational force, ~G = m~g. From the Newtonian mechanics point of view, the gravity acts permanently on the body, meaning that the body cannot be considered as being free. But, in view of the analytical mechanics formalism, this body is considered free, in the sense that no restriction limits its motion. In other words, within the analytical approach, a body that can move freely along any direction in space, and rotate about any axis, is said to be free.