Introduction to Classical Mechanics · Problem 6.31

The Lagrangian method — Morin

Physics — Mechanics · principle-of-stationary-action

Problem

Explicit minimization * For a ball thrown upward, guess a solution for

y

of the form

y(t) = a_2 t^2 + a_1 t + a_0

. Assuming that

y(0) = y(T) = 0

, this quickly becomes

y(t) = a_2(t^2 - Tt)

. Calculate the action between

t = 0

and

t = T

, and show that it is minimized when

a_2 = -g/2