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Unformatted text preview: Massachusetts Institute of Technology Department of Physics Course: 8.09 Classical Mechanics Term: Fall 2006 Quiz 1 October 4, 2006 Instructions Do not start until you are told to do so. Solve all problems. Put your name on the covers of all notebooks you are using. Show all work neatly in the blue book, label the problem you are working on. Mark the final answers. Books and notes are not to be used. Calculators are unnecessary. 2 Useful Formulae Newton and Basic Kinematics: F = p = ma for v c t = t v = v + dt a t =0 t = t = t r = r + v t + dt t dt F ( t ) /m t =0 t =0 Lagrangian and Hamiltonian: L ( q, q ) = T U ; H ( p, q ) = T + U = pq L Euler-Lagrange (without and with constraints): L d L L d L g a = 0; + a = 0 x dt x x dt x x a Polar Coordinates: x = r sin cos ; y = r sin sin ; z = r cos Cylindrical Coordinates: x = r cos ; y = r sin ; z = z Possibly useful integrals: dx dx =...
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This note was uploaded on 03/29/2010 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell University (Engineering School).
- Spring '08