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Question on finding Noethr's theorem and how to find the constant

  1. Apr 1, 2014 #1

    ppy

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    Hi,

    I have attached a file. I am stuck on question 1 on how to find Noether's constant. The solutions are provided however I do not see what they have done. It states that η[itex]^{x}[/itex]=1 and η[itex]^{y}[/itex]=-1 I do not understand how we know this. I can see that [itex]\xi[/itex]=0 because else the -x[itex]^{2}[/itex]-y[itex]^{2}[/itex]-2xy term will not cancel.


    Thanks,
    Melissa Poole
     

    Attached Files:

  2. jcsd
  3. Apr 4, 2014 #2
    Hello,
    in the general case we seek invariance under all coordinate transformations of this type:
    ##\tilde{t} = t + \epsilon \xi##
    ##\tilde{x} = x + \epsilon \eta_x##
    ##\tilde{y} = y + \epsilon \eta_y##

    which in this particular problem is given as
    ##\tilde{t} = t ##, thus ##\xi = 0##
    ##\tilde{x} = x + \epsilon##, thus ##\eta_x = 1##
    ##\tilde{y} = y - \epsilon##, thus ##\eta_y = -1##
     
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