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Limit of zeo mass for a dynamical system

  1. Dec 4, 2011 #1
    Hello All,

    from considering the system of equations (differentiation is mean with respect to time for the function v = v(t) )



    G' = a - v
    v' = (1/m) (G - p (v))

    Very briefly, they characterize the speed of a crack with an "effective mass" m under a generalized force G.

    Dividing the top equation by the lower oneone can conclude that

    dG / dV = m (a - v) / (G- p(v))

    Considering the massless limit m-> 0 one then could obtain

    dG(G- p(v)) = 0.



    After a long preambe, my question : should one not be able to get to the massless limit right from the start by ignoring the term mv' (inertial term) from the start? If I try i do not recover the relationship dG(G- p(v)) = 0

    Any help would really be the most appreciated

    thanks
     
  2. jcsd
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