Introduction to Classical Mechanics · Problem 6.30

The Lagrangian method — Morin

Physics — Mechanics · principle-of-stationary-action

Problem

Dropped ball * Consider the action, from

t = 0

t = 1

, of a ball dropped from rest. From the E–L equation (or from

F = ma

), we know that

y(t) = -gt^2/2

yields a stationary value of the action. Show explicitly that the particular function

y(t) = -gt^2/2 + \epsilon t(t-1)

yields an action that has no first-order dependence on

\epsilon