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Inverse matrix mass computation

  1. Sep 9, 2013 #1
    Hi !
    I've been thinking this problem a whole and I could not find an answer. I want to solve the following problem: suppose I have [itex]N[/itex] mass particles with absolute coordinates [itex] \mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_N [/itex]. Besides, I have the following contraints: for all [itex]i=1,2,\ldots,N-1[/itex], [itex] |\mathbf{x}_{i+1}-\mathbf{x}_i|=L [/itex] where [itex]L[/itex] is a length. In every particle I have a total force over it [itex] \mathbf{F}_i [/itex].

    I used spherical coordinates to express every constraints and parametrize [itex] \mathbf{x}_i [/itex]. However, when I compute the inverse matrix through these method (https://www.dropbox.com/sh/y25m55jpzrh7kqz/Y8EGX25lOQ), I got troubles. Since, I express a generalized coordiante [itex] q_i [/itex] as [itex] \cos q_i = \dfrac{\mathbf{r}\cdot \mathbf{k}}{L} [/itex] and I get: [itex] \dfrac{\partial q_i}{\partial \mathbf r} = -\dfrac{\mathbf{k}}{L\sin q_i}.[/itex] Therefore, when [itex] q_i = 0,\pi [/itex] the denominator is 0, and -><-.

    What can I do ?

    Thanks !!!
     
  2. jcsd
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