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Always a minimum

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data

    For a ball thrown up in the air show that the stationary value of the action is always a global minimum

    2. Relevant equations

    euler lagrange equation and action equation(sorry i don't know syntax here)

    3. The attempt at a solution
    well basically here i used the euler lagrange equation where L=T-V and by using the principle of stationary action figured out that a=g.....by solving the differential equation i found a equaiton of motion for y(t). Thus i sub this into the action equation of S=integral(L)dt and integrate it getting the answer mg^2t^3/6+g^2T^3/2 . and this is where i'm stuck ......i don't know how to show whether this is a global minimum or nor not and also if even my initial steps are correct. If someone could please point me in the right direction it would be great. Thanks.
  2. jcsd
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