On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1936Publisher:JSTORJournal:American Journal of Mathematics, volume 58, page 141 (issn: 0002-9327,

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Authors: Williamson, John;

doi: 10.2307/2371062

On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems

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Abstract

Introduction. Let m be the number of degrees of freedom of a linear conservative dynamical systenm and let the point (q1, q2,9 * , q'Mn Pl p2, . . . p'mt) of the phase space be denoted by x = (xl, x2, , x.2M). A system of 2m ordinary differential equations of the first order, which are homogeneous, linear and do not contain t explicitly, is a canonical system if, and only if, there exists a symmetric matrix A, such that the differential equations may be written in the form (i) Bdx/dt =Ax,

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