[PTR/CM-ALL]

[PTR/CM/02001]  Generalized coordinates for a system are a set of variables having the following properties.

1. The generalized coordinates \(\qbf=\{q_1,q_2,\ldots, q_n\}\), along with their time derivatives,\(\dot{\qbf}=\{\dot{q}_1,\dot{q}_2,\ldots, \dot{q}_n\}\) , describe the state of the system at a given time completely with \(n\) degrees of freedom.
2. The generalized coordinates are independent, there is no constraint between them.
3. The position vectors of all the bodies can be expressed as functions of generalized coordinates

[PTR/CM02001] Lagrangian} of a system is given by
\begin{equation}
 L = \text{K.E.} - \text{P.E.}
\end{equation}
expressed as functions of generalized coordinates \(q\) and their time derivatives \(\dot{\qbf}\).