Newtonian Gravity with Velocity Verlet and OpenGL (2016)

Re:Newtonian Gravity with Velocity Verlet and OpenGL (2016) by aroman_ro on Thursday March 14, 2019 @06:17PM (#19394405)

The biggest is that in real molecular dynamics simulation you need the position and velocity at the same time. If you want to calculate the total energy, for example, you need both positions and velocity at one time moment. It's not a big deal for a simple project to simply average the 'before' and 'after' velocities... but again, those are tiny details. There is the initial state issue, again, a tiny detail. You may find more...

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Re:Newtonian Gravity with Velocity Verlet and OpenGL (2016) by jules on Thursday March 14, 2019 @06:54PM (#19394711)

With leapfrog you can use x + v dt/2 for the positions to calculate the energy. Or use this update rule:

    x += v*dt/2
    v += a(x)*dt
    x += v*dt/2

This gives you the x,v at the same time, yet still doesn't require storing the accelerations. The acceleration calculation can imperatively update v :)

In fact, if you call that update leapfrog(dt), then you can get a fourth order symplectic method like so:

    leapfrog(c1*dt)
    leapfrog(c2*dt)
    leapfrog(c1*dt)

Where c1,c2 are particular coefficients which you have to ask Yoshida.

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Re:Newtonian Gravity with Velocity Verlet and OpenGL (2016) by aroman_ro on Thursday March 14, 2019 @07:42PM (#19395048)

As I said, tiny details :)

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