Virial theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force, with that of the total potential energy of the system. Mathematically, the theorem states that ⟨ T ⟩ = − 1 2 ∑ k = 1 N ⟨ F k ⋅ r k ⟩ , {\displaystyle \langle T\rangle =-{\frac {1}{2}}\,\sum _{k=1}^{N}\langle \mathbf {F} _{k}\cdot \mathbf {r} _{k}\rangle ,} where T {\displaystyle T} is the total kinetic energy of the N {\displaystyle N} particles, F k {\displaystyle F_{k}} represents the force on the k {\displaystyle k} th particle, which is located at position rk, and angle brackets represent the average over time of the enclosed quantity.