Classical Dynamics of Particles and Systems · Problem 6-15

Hamilton's Principle—Lagrangian and Hamiltonian Dynamics — Marion & Thornton

Physics — Mechanics · calculus-of-variations-functional-minimization

Problem

(a) Find the curve

y(x)

that passes through the endpoints

(0, 0)

and

(1, 1)

and minimizes the functional

I[y] = \int_0^1[(dy/dx)^2 - y^2]dx

. (b) What is the minimum value of the integral? (c) Evaluate

I[y]

for a straight line

y = x

between the points

(0, 0)

and

(1, 1)