Question

Write the expression of generalized force, velocity and kinetic energy

Answer 1

(i)

$$Q_j = \displaystyle\sum_{i=1}^nF_i * {\delta r_i \over \delta q_i}, j = 1, 2, ... , m$$

(ii)

$$Q_j = \displaystyle\sum_{i=1}^nF_i * {\delta V_i \over \delta \overset{\cdot}{q}_j}, j = 1, 2, ... , m$$

(iii)

If

$$E_k = {mv^2 \over 2}$$

$$E_k = E_{total} - E_p = E_{total} - mgh$$

We have

$${d \over dt}({\delta L \over \delta \overset{\cdot}{q}_i}) - {\delta L \over \delta q_i} = Q_i^n$$

In general, generalized forces can be considered as variations for the generalized coordinate in the term expression for virtual work.

Potential forces with all non-potential are taken into account. It is expressed through the Lagrange function L.