关键词: 基础力学, 动力学逆问题, 非保守系统, 非完整系统, Bertrand定理

Abstract: A dynamical inverse problem of a nonholonomic non-conservative system in phase space was studied. The differential equations of motion were established for non-conservative and nonholonomic non-conservative systems in phase space，respectively. A first-order ordinary differential equation was obtained by differentiating a known integral of the system with respect to time and introducing the Erugin function. Under two circumstances of which the non-conservative forces only rely on generalized coordinates and only rely on generalized momentum, the algebraic equations for determining the non-conservative forces were obtained by the first-order ordinary differential equation and using the differential equations of motion of the systems. The non-conservative forces of the systems can be determined by solving the above algebraic equations. Some examples were given to illustrate the application of the results.