Analytical Mechanics

Definition

A formulation of the laws of mechanics based on the geometric concept of configuration space. In this approach, forces (or, more precisely, generalized forces) are considered as linear operators on vectors tangent to the configuration space (virtual displacements, or virtual velocities).

Description of the Theory

The concept of configuration space is briefly discussed in the article on classical mechanics (q.v.), and the use of generalized coordinates has been introduced in the article on the principle of virtual work (q.v.). To effect the transition to analytical mechanics the so-called principle of D’Alembert, briefly discussed in the article on statics (q.v.), may be invoked. According to this principle the equations of motion of a system can be regarded as equilibrium equations that include fictitious inertia forces. Applying this idea to the principle of virtual work, the virtual work of the forces of inertia associated with the free motion of a single particle in...