Qmechanic in this answer says that only Dirichlet b.c.s are consistent with static solutions of point particle mechanics. Why is this so?
E.g. The standard classical harmonic oscillator problem with b.c. $x(t_i)=0,\dot{x}(t_i)=0$ is not a Dirichlet b.c. but still returns the static solution $x(t)=0$. What is my mistake here?
