Only two variables are needed, since the motion occurs in a plane. Substituting the second expression into the first and rearranging gives m r ˙ ˙ 2 = 2 E − − L 2 m r 2 + 2 G m M r = 2 E − − 1 r 2 ( L 2 m − − 2 G m M r ) , 1 2 m r ˙ ˙ 2 = E − − U eff ( r ) , where U eff ( r ) = L 2 2 m r 2 − − G m M r is the effective potential. The original two-variable problem has been reduced to a one-variable problem. For many applications the effective potential can be treated exactly like the potential energy of a one-dimensional system: for instance, an energy diagram using the effective potential determines turning points and locations of stable and unstable equilibria. A similar method may be used in other applications, for instance determining orbits in a general relativistic Schwarzschild metric.