Dimensional Analysis

Dimension

The dimension of the configuration space is called the number of degrees of freedom.

Buckingham Theorem

If the behaviour of a system is governed by physical variables, which depend upon fundamental independent quantities, the system evolution may be described by dimensionless parameter groups.

e.g. Suppose we have the following equation of motion of dimensional coordinates and : Now define and , then we can convert the above to the following dimensionless equation:In the above dimensionless equation we can freely set one of the coefficients.