Finding Generalized Forces by Use of Partial Derivatives of Energy Functions

A general conservative system may be considered to be represented by n(generalized) ports at which energy can enter the system; two generalized variables are associated with each port, the generalized force variable and the generalized coordinate variable. It is shown that the generalized force exerted on the system by the ith port at any given point in the system may be expressed in terms of the rate at which energy enters the system because of a change in the ith coordinate variable. The result is then employed to examine two classic problems which are frequently dealt with incorrectly.