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Optimized Path of a Particle experiencing a Time - Varying Force

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Given a force F(t), calculate the optimized path the particle, initially at a, should take to reach point b. Consider the particle to travel in a one - dimensional space only (x axis). The particle has kinetic energy only.


    2. Relevant equations
    L = T - U
    [itex]\frac{\partial L}{\partial x_{i}} - \frac{d}{dt} \frac{\partial L}{\dot{x}_{i}} = 0[/itex]


    3. The attempt at a solution
    If the particle is only purely kinetic, then the first term of the equation is zero and the second term is only [itex]\frac{d}{dt} mv(t)[/itex] which implies that the velocity is constant in time. I also do not know if this will give the optimized path of the particle and how to implement it...
     
  2. jcsd
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