If the potential does not depend on velocities, the corresponding force is simply the negative of the gradient of the potential. This is a situation that occurs frequently: constant gravitational field, Coulomb-type or Newtontype law, Hooke’s law for springs.
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© 2009 Springer Science+Business Media B.V.
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Gignoux, C., Silvestre-Brac, B. (2009). Lagrangian Systems. In: Solved Problems in Lagrangian and Hamiltonian Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2393-3_2
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