Work, Line Integral and Potential

  • Markus Antoni


The work or energy W, which is necessary to move a unit mass in a force field \(\varvec{F}\) or \(\varvec{G}\), is usually depending on the chosen path \(\varvec{\Psi }(t)\) between the points \(\varvec{A}\) and \(\varvec{B}\). The work is then evaluated by a line integral
$$\begin{aligned} W&= \int \limits _{t_{A}}^{t_{B}} \Big (\varvec{F}(\varvec{\Psi })\Big )^\top \varvec{T} \mathrm {d}t,\\ W&= \int \limits _{t_{A}}^{t_{B}} \Big (\varvec{G}(\varvec{\Psi })\Big )^\top \varvec{T} \mathrm {d}t, \end{aligned}$$

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of GeodesyUniversity of StuttgartStuttgartGermany

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