If you would just look at the equation of motion/equilibrium (so without looking at the physical situation), are you able to determine whether an equilibrium configuration is stable or unstable?
@JurnanSchilder4 жыл бұрын
Yes you are! For this you need to have the nonlinear EoM. Then you determine the equilibria. Then you can linearize the EoM around an equilibrium and compute the eigenvalues (think: natural frequencies). If at least one of the eigenvalues have a positive real part, the general solution will contain an exponential function with a positive exponent. This will blow up in time and thus represents unstable behaviour. If all eigenvalues are negative (or complex with a negative real part) we have a stable solution. Eigenvalues that are purely imaginary represent undamped vibrations. You could do this linearization and solve the EVP for every equilibrium configuration to determine which of them are stable and which of them are not.
@abhishekpg96152 жыл бұрын
Should we include the force mg in equation of motion because if we consider the static deflection then mg and static deflection would cancel out right?