# Lagrange with Higher Derivatives (Ostrogradsky instability) [duplicate]

In class our teacher told us that, if a Lagrangian contain $$\ddot{q_i}$$ (i.e., $$L(q_i, \dot{q_i}, \ddot{q_i}, t)$$) the energy will be unbounded from below and it can take any lower values (in other words be unstable). In this type of systems can we show that the energy is conserved ? Or in such system does energy conservation is applicable ?

Not enough reputation to comment, sorry. It should still be true that if there is no explicit $$t$$-dependence and the potential is a function of $$q$$, then the Lagrangian conserves energy.