Classical Dynamics of Particles and Systems · Problem 6-17

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

Physics — Mechanics · lagrange-multipliers-ellipse-rectangle

Problem

The corners of a rectangle lie on the ellipse

(x/a)^2 + (y/b)^2 = 1

. (a) Where should the corners be located in order to maximize the area of the rectangle? (b) What fraction of the area of the ellipse is covered by the rectangle with maximum area?

Related theory

Lagrange Multipliers

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