Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow. As applications, the results are applied to the analysis of dissipative Hamiltonian systems arising from circuit simulation and incompressible flow.

翻译：正在研究具有对称性的线性时间差值对数方程。我们处理的结构是自对称和自对称系统。提出并使用一致性下的地方和全球金刚石形式,将与差异方程相关的流动的几何特性分类为共振或统正方圆流。作为应用,这些结果应用于分析电路模拟和不压缩流产生的散散散的汉密尔顿系统。