- #1
astrof
- 16
- 0
The problem is a simple n-body problem:
there is n charged particles - electrons, protons, or other particles;
we have the initial parameters: a mass, charge, position, velocity, at a time t = 0.
In a standard (classical) numerical computation of the n-body problem I can use any numerical method based on a force, say:
F = am = k/r^2; for gravity and for the charged bodies is the same...
But I want to apply the SR model.. so, what is a difference - the force formula has other form - how is it?The SR equation is still: E = Ek + Ep
the Ek has other form: [tex]E_k = mc^2(\gamma-1)[/tex]
and the potential Ep is the same: Ep = k/r;
but what is the force which I want to apply in every step of the simulation?
F_ij = m_i ai = ... ?
there is n charged particles - electrons, protons, or other particles;
we have the initial parameters: a mass, charge, position, velocity, at a time t = 0.
In a standard (classical) numerical computation of the n-body problem I can use any numerical method based on a force, say:
F = am = k/r^2; for gravity and for the charged bodies is the same...
But I want to apply the SR model.. so, what is a difference - the force formula has other form - how is it?The SR equation is still: E = Ek + Ep
the Ek has other form: [tex]E_k = mc^2(\gamma-1)[/tex]
and the potential Ep is the same: Ep = k/r;
but what is the force which I want to apply in every step of the simulation?
F_ij = m_i ai = ... ?