Q:

Hi,I am trying to understand if in a system of 3 point like particles (minimum possible to have torsion) under potential that depend only on pairwize distances (like gravitation or spring between each pair) it is possible to have a total average non-zero torsion.I did some numerical simulations with random starting conditions and the total accumulated torsion varies however it is always close to zero.is there a reason why it will always be zero? if no can you think of a trajectory (and potential) which will have substantially non-zero average torsion over long runs?Thanks you very much

- Ohad Frand (age 39)

israel

- Ohad Frand (age 39)

israel

A:

The total torque is exactly zero. In general that's true for any closed system- angular momentum is conserved. In general, however, you have to include electromagnetic fields and other non-obvious components of the angular momentum. In this case, with purely central forces between the masses, the obvious angular momentum from their motions is conserved, with no need for other terms.

The proof is essentially the one Newton used to explain Kepler's Second Law. Newton's Third Law furantees that the forces in any pair are equal and opposite. Since they are along the line of centers between the two objects in the pair, they have equal lever arms around any point and thus give zero net torque.

Numerical simulations have a little jitter from the finite time intervals and from rounding errors. So the numerical answers aren't exact.

Mike W.

*(published on 08/05/2016)*