Elliptic bob path at zero horizontal momentum
= Elliptic bob path at zero horizontal momentum
{title2=$(X-X_c)^2/[lm_1/(m_1+m_2)]^2+Y^2/l^2=1$}
Zero horizontal <momentum> fixes the horizontal <centre of mass>. The bob coordinates become $X=X_c+lm_1\sin\phi/(m_1+m_2)$ and $Y=-l\cos\phi$. Eliminating the angle gives an <ellipse>; an ordinary <oscillation> traverses only its permitted arc. The support counter-moves, so the bob's path differs from the circle about a fixed pivot.