//for a small dt, the newtonian method is stable
//providing that forces and acceleration are both insignificant
public MassParticle Elapse(Vector force, double dt)
{
var acc = force / Mass;
var dp = Velocity * dt + acc * dt * dt * 0.5;
var dv = acc * dt;
var newm = new MassParticle();
newm.Velocity = Velocity + dv;
newm.Position = Position + dp;
newm.Mass = Mass;
return(newm);
}
//add particle and assign a random position if not exist
public void AddParticle(Vertex v)
{
AddVertex(v);
if (HasParticle(v))
{
return;
}
var newp = new MassParticle();
newp.Mass = m;
newp.Velocity = Vector.Zero;
newp.Position.X = (RNG.NextDouble() * 2 - 1) * L * 10;
newp.Position.Y = (RNG.NextDouble() * 2 - 1) * L * 10;
Particles[v] = newp;
}