2. The Hamiltonian of a certain rheonomic system is given by H(q. p, t) = wq (e Bt sin? p + eBt cos2 p) w, 3 = constants 2.1. Use the generating function F(p, P. t) = -mwe-Ftp2 tanp to find the transformation equations: q = q(Q, P, t) P = P(Q, P, t) 2.2. Use the transformation to find the equations of motion of the system. 3. One Valentine's morning, you saw your crush wearing a gorgeous T-shirt with the following equation printed on it ox X = JVH + at 3.1. What would you say to impress your crush? 3.2. Assuming your first remark sparks an intimate conversation, what essential ideas will you mention to substantiate the derivation of the equation. 3.3. What example would you present to demonstrate the application of the equation