Classical Mechanics (Kibble & Berkshire) · Problem 12.14

The calculus of variations and Hamilton's principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · lagrangian-mechanics-velocity-dependent-potential

Problem

Suppose a particle is subjected to a time dependent force of the form

\boldsymbol{F} = f(t) \operatorname{grad} W(\boldsymbol{r})

. Show that this force can be represented by the time dependent potential

U = -f(t)W(\boldsymbol{r})

. What is the value of

U

when

\boldsymbol{F} = f(t)\boldsymbol{i}