A canonical form of the equation of motion of linear dynamical systems

作者：Kawano Daniel T; Salsa Rubens Goncalves Jr; Ma Fai^*; Morzfeld Matthias

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2018, 474(2211): 20170809.

DOI：10.1098/rspa.2017.0809

• linear systems
• equations of motion
• decoupling
• viscous damping

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

• 出版日期2018-3