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

Daniel T. Kawano | Zendy; Rubens Gonçalves Salsa | Zendy; Fai Ma | Zendy; Matthias Morzfeld | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Daniel T. Kawano,

Rubens Gonçalves Salsa,

Fai Ma,

Matthias Morzfeld

Publication year - 2018

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2017.0809

Subject(s) - canonical form , invertible matrix , mathematics , riccati equation , linear differential equation , mathematical analysis , differential equation , diagonal , motion (physics) , coefficient matrix , linear system , ordinary differential equation , equations of motion , linear motion , linear equation , classical mechanics , pure mathematics , physics , geometry , eigenvalues and eigenvectors , quantum mechanics

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research