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2. Hamilton's Principle is a statement that trajectories are a stationary function of the action integral. Consider the simple case of a single function y(t) with kinetic energy T = %y'(t)2 with potential energy U (y) E 02(R). Consider the action integral on the time interval [0, b]. Consider variations 3; + '1} on the stationary trajectory y With the same endpoints so that the set of admissible variations is A = {v E Cl[0,b]| 11(0) = 12(1)) = 0}. Show that if b is suiciently small, then the stationary trajectory is a minimum. The following inequality will be useful: 71.2 b b b2 0 v(t)2dt/0 t)(t)2dt, for ailveA. (1) (This is Wirtinger's Inequality, and also one version of Poincar's Inequality.)