Premium
On the nullity of homogeneous linearized kinematic and equilibrium equations of a system of supported and connected rigid bodies
Author(s) -
Flajs Rado
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900220
Subject(s) - kinematics , statics , homogeneous , mathematics , matrix (chemical analysis) , interpretation (philosophy) , work (physics) , virtual work , simultaneous equations , mathematical analysis , classical mechanics , differential equation , physics , computer science , finite element method , thermodynamics , materials science , combinatorics , composite material , programming language
Abstract This paper deals with homogeneous linearized kinematic equations and the equilibrium equations of systems of supported and connected rigid bodies, the type of which were encountered during the undergraduate course of Statics within the first year of the study of Civil Engineering at the University of Ljubljana. In the paper the very fundamental relation nullity( A ) = nullity( B T ) is proven using the well‐known virtual work principle. Here, matrices A and B denote the matrix of the homogeneous linearized kinematic equations and the matrix of the equilibrium equations, respectively. Since the well‐known equilibrium equations A T x ⇀ = F ⇀ could potentially lack a physical interpretation [1], a new proof for a smaller set of the equilibrium equations, preferable in practical and pedagogical sense [2,3], is presented.