Basic Concepts in Analytical Mechanics

The description of a mechanical system need not be shackled in the framework of the cartesian coordinate system. In this section it is discussed how the description can be more generalized in approach. The choice of the coordinates depends also on another property of a system termed as the degrees of freedom. Degrees of Freedom: The degrees of freedom of a system is the minimum number of independent quantities necessary for a complete description of the configuration. Figure 2.1 shows the degrees of freedom of some systems. When a particle is constrained to move along a fixed trajectory obviously only one quantity giving the distance from the starting point along the prescribed path fixes the position of the particle, and such systems have a single degree of freedom. In Fig. 2.1a the system with a single particle constrained to move in the x-y plane has 2 degrees of freedom since it has to satisfy the constraint equation \(z=0.\) .