  It is known that any nondegenerate Lagrangian containing time derivative
terms higher than first order suffers from the Ostrogradsky instability,
pathological excitation of positive and negative energy degrees of freedom. We
show that, within the framework of analytical mechanics of point particles, any
Lagrangian for third order equations of motion, which evades the nondegeneracy
condition, still leads to the Ostrogradsky instability. Extension to the case
of higher odd order equations of motion is also considered.
