# Equilibrium and stability

• Engineering
curiousPep
Homework Statement:
How can I find the condition for the system to be equilibrium and how to check if these solution are stable or not?
Relevant Equations:
Equations of motion
When I use Lagrange to get the equations of motion, in order to find the equilibrium conditions I set the parameters q as constants thus the derivatives to be zero and then calculate the q's that satisfy the equations of motion obtained.
In ordert to check about stability I think I need to add some small perturbation, thus q' = q+dq. Then how can I check if the solutions are stable or not?