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Optimized Path of a Particle experiencing a Time - Varying Force
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[QUOTE="ecastro, post: 4127614, member: 440873"] [h2]Homework Statement [/h2] 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. [h2]Homework Equations[/h2] L = T - U [itex]\frac{\partial L}{\partial x_{i}} - \frac{d}{dt} \frac{\partial L}{\dot{x}_{i}} = 0[/itex] [h2]The Attempt at a Solution[/h2] 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... [/QUOTE]
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Optimized Path of a Particle experiencing a Time - Varying Force
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