经典阻尼系统响应的辛解析解

An Analytic Symplectic Solution for Classical Damping System Response

突破了辛方法只能用于守恒系统的限制。提出了一种藉助于无阻尼系统辛解法以求解经典阻尼系统响应的方法。对于无阻尼系统的辛解法进行了分析,论述了该法与常规方法的一致性。算例结果表明,所提方法有效、可行。

Any real physical process without dissipation can be expressed as a Hamilton system.The research of Hamilton Mechanics can not be done without Symplectic Geometry,and the calculation of Hamilton Mechanics can not be done without Symplectic Method.The limitation that Symplectic Method can only be applied to a conservative system is broken through by authors of this paper.Therefore,another small door for the application of Symplectic Method was opened.The difficulty of Symplectic Method to find the response of a damped system is expounded,and a Symplectic Method to get the response of the system with classical damping is proposed.An analysis of Symplectic Method for undamped system response is carried out,then,the consistency between the conventional solution and Symplectic solution is demonstrated as well.Results of examples show that the method proposed in the paper is efficient and feasible.