The vector force field F=(yi,-xj) has a curl of -2. The acceleration of a particle in space is given by: ax=y/m ay=-x/m This vector field has a divergence of 0. Will particles in this vector FORCE field move in circles or will they spiral outwards in a crazy fashion? My conundrum is this, the acceleration of the particles is never towards the center, therefor there is no centripetal acceleration, so how can these particles move in discreet circles?
Does this reasoning make sense or am I doing a nested substitution:
r=Sqrt[x^2+y^2] r=Sqrt[((1/2)ax*t^2)^2 + ((1/2)ay*t^2)^2] r=(1/2)Sqrt[t^4 (ax^2 + ay^2)] r=(1/2)Sqrt[t^4 a^2] r=(1/2)at^2