**Start with Newton’s Second Law** Let \(\vec F_{\alpha}\) be total force acting on \(\alpha ^{th}\) particle. The equations of motion are $$\vec F_α = \frac d {dt} \vec p_α, \hspace{.5em} α = 1, ... \hspace{5em}(2)$$ \(\vec p_{\alpha} =\) momentum of \(α^{th}\) particle. $$(or) \hspace{.5em} \left(\vec F_α - \frac d {dt} \vec p_α \right) = 0 \hspace{5em} (3)$$ For small displacements \(\delta \vec r_{\alpha}\), we have $$\left(\vec F_α - \frac d {dt} \vec p_α \right) . \delta \vec r_α = 0 \hspace{5em} (4)$$ Summing over all particles $$\sum _{α=1}^N \left(\vec F_α - \frac d {dt} \vec p_α \right).\delta \vec r_α = 0 \hspace{5em} (5)$$ **4.1 Net force on a particle is a sum of external forces and forces due to constraint** We write total force \( \vec F_{\alpha}\) as $$\vec F_α = \vec F_α^{(e)} + \vec f_α \hspace{5em} (6)$$ where \( \vec F_{\alpha}^{(e)}\) is total force on \(\alpha^{th}\) particle excluding the force due