Given an equation $F(x)$ that represents the magnitude of some force $F$ that varies with distance from the origin, is it possible to derive the equation of motion $p(t)$ of a point particle $P$ placed within this force field with arbitrary initial position and initial velocity?
2026-04-01 06:12:44.1775023964
Central Force Problem
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Sure, just solve: $m\ddot{p}=F(p)$, with $p(0)=p_0$ and $\dot{p}(0)=v_0$.