- #1
Soren4
- 128
- 2
For a conservative force [itex]\vec{F}=-\vec{\nabla} U \implies dW=-\vec{\nabla}U \cdot d\vec{s}[/itex]
Where [itex]d\vec{s}[/itex] is the infinitesimal vector displacement.
Does the following hold?
[itex]-\frac{\partial U}{\partial \vec{s}}=-\vec{\nabla} U \cdot d\vec{s}=d W[/itex], i.e. the infinitesimal work is minus the directional derivative of [itex]U[/itex] in the direction of [itex]\vec{s}[/itex].
Where [itex]d\vec{s}[/itex] is the infinitesimal vector displacement.
Does the following hold?
[itex]-\frac{\partial U}{\partial \vec{s}}=-\vec{\nabla} U \cdot d\vec{s}=d W[/itex], i.e. the infinitesimal work is minus the directional derivative of [itex]U[/itex] in the direction of [itex]\vec{s}[/itex].