WOLFRAM|DEMONSTRATIONS PROJECT

Electric Dance: A Symmetrical Three-Body Coulombian System

​
time
t
0.0
initial position (slow response)
SubscriptBox[\(θ\), \(\( \)\(0\)\)]​°
30
animation rate
1
t
max
60
show full orbits traces
show dynamic orbits traces
U
0
-
1
3
P
0
{0.866,0.5}
r
0
1.
θ
0
= 30.°
t0.0
This Demonstration considers a three-body Coulombian system with high symmetry.
Three charged particles, two positive (blue) and one negative (red), are released from rest at the vertices of an isosceles triangle (equilateral in the initial setting). Assume that the particles have the same charge (apart from sign), the same mass, and that only electrostatic forces act on them.
The system dynamics are driven by Coulombian attractive/repulsive forces. Given the strong symmetries in the initial conditions and the conservation of energy and momentum, the solution for this system can be reduced to just a couple of differential equations because the position/velocity of one of the blue particles is enough to determine the positions/velocities of the other two.