Maple activities for circular motion stability

• Take the book's choice of U = -k/r exp(-r/a)
• write out Ueffo = l^2/2m/r^2 -k/r exp(-r/a)
• let b = l^2/m and write Ueff1 = b/2/r^2 - k/r exp(-r/a)
• set eq1:= diff(Ueffo,r) = 0;
• let bo be the solution to eq1
• substitute r=ro in bo and call this b1
• ro is the radius for circular motion
• substitute b1 for b in Ueff1, calling it Ueff2
• Now Ueff2 is a function of r, and k and a and ro
• you can plot Ueff2 if values are substituted for k, a, and ro.
• let k=1 and a=1 and then do a succession of plots with different values of ro
• check with the book on page 326 and make sure the minimum comes at the correct value of ro (namely the one you put in)
• it is claimed that if ro is greater than 1.62a there will be no stable motion
• this means no minimum in the effective potential