Abstract: By using the Lagrangian approach to classical mechanics，we investigate the condition of static equilibrium

and the continuum dynamics，respectively. By using Hamiltonian approach，we introduce the distinct

point of equilibrium as well as the stable ensemble distribution，which makes sense in the scope of statistical mechanics，

in the phase space.The examples show that the concept of acceleration is disenchanted in the framework of

analytical mechanics.Also，the so-called“equilibrium states”are found to be realized by the different ways from

the case of Newtonian approach.

Key words: Lagrangian and Hamiltonian approaches, generalized acceleration, equilibrium state