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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Gauss%27s_principle_of_least_constraint


00:04:13 1 Hertz's principle of least curvature
00:10:26 2 See also



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SUMMARY
=======
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 accelerations of a mechanical system of



N


{\displaystyle N}
masses is the minimum of the quantity




Z





=



d
e
f







∑

k
=
1


N



m

k




|





d

2




r


k




d

t

2





−




F


k



m

k





|


2




{\displaystyle Z\ {\stackrel {\mathrm {def} }{=}}\ \sum _{k=1}^{N}m_{k}\left|{\frac {d^{2}\mathbf {r} _{k}}{dt^{2}}}-{\frac {\mathbf {F} _{k}}{m_{k}}}\right|^{2}}
for all accelerations



{




d

2




r


k




d

t

2





}


{\displaystyle \{{\frac {d^{2}\mathbf {r} _{k}}{dt^{2}}}\}}
satisfying the imposed constraints, where




m

k




{\displaystyle m_{k}}
,





r


k




{\displaystyle \mathbf {r} _{k}}
and





F


k




{\displaystyle \mathbf {F} _{k}}
represent the mass, position and applied non-constraint forces of the





k

t
h





{\displaystyle \mathrm {k^{th}} }
mass.
Note that the set of accelerations satisfying the imposed constraints is in general dependent on the current state of the system,




{
(
...