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I have a problem with homework from my "Basics of theoretical phisics" class.

1. The problem statement, all variables and given/known data

I have to find a trajectory of a particle in field of force:

[tex] F = - \frac{\alpha}{x^2} [/tex]

2. Relevant equations

I was said to use:

[tex] F = \dot{p} = \frac{dp}{dt} [/tex] and [tex] p=mv\gamma [/tex]

where [tex]\gamma[/tex] is: [tex]\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} [/tex] and m is rest mass.

3. The attempt at a solution

[tex]\dot{p} = \frac{dp}{dt}=m \frac{d (v\gamma)}{dt} = m (\dot{v}\gamma + v \dot{\gamma}) [/tex]

[tex] \dot{\gamma} = -\frac{1}{2} (1-\frac{v^2}{c^2})^{-3/2} \frac{2v}{c} \dot{v} = \dot{v} \frac{v}{c^2} \gamma^3 [/tex]

[tex] \dot{p} = m(\dot{v} \gamma + v \dot{v} \frac{v}{c^2} \gamma^3) = m \dot{v} \gamma (1+ \frac{v^2}{c^2} \gamma^2)= m \dot{v} \gamma^3 [/tex]

[tex] v=\dot{x} , m \dot{v} \gamma^3 = m \ddot{x} \gamma^3 = -\frac{\alpha}{x^2} [/tex]

[tex] \ddot{x} x^2 \gamma^3 = -\frac{\alpha}{m} [/tex]

Now I have a problem with that equation. Any ideas how to solve it and get [tex] x(t) [/tex]?

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# Homework Help: Trajectory of a particle in a field (special relativity)

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