Gauss's principle of least constraint

The principle of least constraint is another formulation of classical mechanics enunciated by Carl Friedrich Gauss in 1829.

The principle of least constraint is a least squares principle stating that the true motion of a mechanical system of ${\displaystyle N}$ masses is the minimum of the quantity

for all trajectories satisfying any imposed constraints, where ${\displaystyle m_{k}}$, ${\displaystyle \mathbf {r} _{k}}$ and ${\displaystyle \mathbf {F} _{k}}$ represent the mass, position and applied forces of the ${\displaystyle \mathrm {k^{th}} }$ mass.

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