The recoil system of a gun system is essentially a critically damped system to absorb the recoil force. Light weight and optimum bulk of an artillery gun system can be achieved if the recoil force and recoil length of the gun system are simultaneously minimized. This can be achieved if the perimeter of the recoil travel diagram is minimum. The theorem presented and proved in this short note seeks to elucidate this principle. The proof of the theorem has been developed by using the metric tensor approach to derive the equation of geodesics using the Euler or Lagrange equation in Riemann space.
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