The Traction Problem in Elastodynamics

In continuum mechanics.Cauchy's six equations

are incomplete[1] and the famous Cauchy's laws of motion

where ,ρb,T and divT are continuous are also incomplete^[2].The first six equations are incomplete because the geometrical representation of deformation at a given point is as yet incomplete^[3],and the last two laws are incomplete because b,T and divT are frame-indifferent,but is not,and T is a symmetric,as Cauchy interpreted himself.Therefore,we say,the last two laws can't accommodate to the asymmetric tensor.The purpose of this paper is to complete Cauchy's laws of motion by postulating an asymmetric tensor for the underlying traction field of 3-dimensional space on a general framing.