Once the above is established it is possible to develop a formulation that involves the general motion of the system rather than individual motion of each entity.  A device first thought of by James Bernoulli, and developed by D'Alembert accomplishes this feat.  Its content is strictly mathematical and leads to the Lagrange equations of motion for conservative holonomic systems.

                                                                 (3.17)

where    .

For an example of the derivation see Goldstein [1959, 14-18].

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