於古典力學範疇，通常先設定某一 Lagrangian 泛函為系統的行動能量，再利用變分法求其最小值而決定該系統的運動方程式。倘若我們假定平方反比定律為大自然的最佳控制手段，試問其對應的行動能量為何?本文以二個物體的平面運動為分析對象，來回答此一問題。首先利用
Pontryagin 最小原則，推導發現該行動能量須滿足特定的偏微分方程。此一方程的解雖有無限多組，然其中一組的解為該系統的行動能量是總能量，所顯示的物理意義為大自然若採取平方反比定律為最佳控制器，其目的在維持物體沿特定軌道運動的總能量為固定。文章最後，將此問題推廣到多體運動的情形，得到一組偏微分，在一般情形下不易求解。

The usual way in developing the formulation for classical mechanics is to define the Lagrangian for the action first and then the equation of motion is obtained by using calculus of variation to minimize the
action. If we recognize the inverse square law being an optimal controller presented by nature, what is the corresponding action (or Lagrangian) for it? First of all, a planar motion of two bodies is considered. An optimal control problem is then formulated with a presumed unknown Lagrangian. By using Pontryagin minimal principle to minimize the action, a partial differential equation for the Lagrangian is obtained and
solved. For this action, it can be verified directly that the inverse square law is the corresponding optimal controller. Finally, the generalization of this mechanization is presented for more complicated dynamical systems. This type of problem is considered as an inverse problem from the optimal control theory point of view.