Unformatted text preview: center, so that it slides down the hemisphere without friction. Describe the subsequent motion of the particle. [See p. 47 of GPS.] y ˆ g − 4. Write down a Lagrangian for each of the following situations, in terms of an appropriate set of generalized coordinates. Use Lagrange multipliers as needed. What are the symmetries? Give expressions for the corresponding conserved quantities. (a) A particle of mass m moving on the frictionless surface of sphere. (b) Two particles constrained to move on the surface of a sphere, interacting gravitationally with each other. (c) A charged particle moving in a uniform electric field. (d) A charged particle moving in a uniform magnetic field. In this case, use Noether’s Theorem to derive the conserved momenta, angular momentum (in the direction parallel to the magnetic field), and energy....
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 Fall '08
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 mechanics, Force, General Relativity, Fundamental physics concepts, Lagrangian mechanics

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