Based on the analysis of establishing dynamic equations by using Newton mechanics, Lagrange and Hamilton mechanics, a new idea of establishing dynamic equations under the framework of energy conservation is proposed. Firstly, the use of Newton’s second law to derive wave equations of motion is introduced. Secondly, the Lagrange equation, Hamilton canonical equation, and the corresponding dynamical equations in a continuum are derived by using Hamilton’s variational principle. Thirdly, under the framework of energy conservation, the Lagrange equation, Hamilton canonical equation, and acoustic dynamics equation of continuum are established, and the results are proved to be consistent with those derived from classical mechanics. Some of fuzzy understandings when using Hamilton's variational principle to establish Lagrange’s equation and Hamilton’s canonical equation, are clarified. A series of dynamical equations established under the framework of energy conservation provides alternative way to characterize and represent the propagation characteristics of wave motions in various complex media without involving the variational principle of functional extremum. Finally, as an application example, the differential equation of dynamics in viscoelastic medium is given under the framework of energy conservation.
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