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A diagram showing a path P that an object might take from an initial point with position \vec{r}_i to a final point with a position \vec{r}_f. The integral of displacement dotted into momentum along this path is just twice the integral of its kinetic energy from the initial time t_i to the final time t_f.

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A diagram showing a path P that an object might take from an initial point with position \vec{r}_i to a final point with a position \vec{r}_f. The integral of displacement dotted into momentum along this path is just twice the integral of its kinetic energy from the initial time t_i to the final time t_f.
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Robert McNees (mcnees@mastodon.social)'s status on Thursday, 28-Sep-2023 14:56:23 UTC Robert McNees
in reply to

By 1744, Maupertuis extended this idea to the motion of material objects.
He defined an object's “action" as the integral of momentum along its path, or the time integral of its "vis viva" (2 x kinetic energy) from start to finish.
Maupertuis proposed that Nature acts to minimize this quantity.

In conversation about a year ago from mastodon.social permalink