Bonnet's theorem

In classical mechanics, Bonnet's theorem states that if n different force fields each produce the same geometric orbit (say, an ellipse of given dimensions) albeit with different speeds v₁, v₂,...,v_n at a given point P, then the same orbit will be followed if the speed at point P equals

${\displaystyle v_{\mathrm {combined} }={\sqrt {v_{1}^{2}+v_{2}^{2}+\cdots +v_{n}^{2}}}}$