set7 - Department of Physics The Ohio State University...

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Department of Physics Prof. R. Bundschuh The Ohio State University Seventh Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 31 no class, Jun 9 9:30am-11:18am Fnal exam Due date: Thursday, May 20 17. Lagrangian for non-potential force 12 points As an example of a Lagrangian that does not correspond to motion under the in±uence of a force that can be represented by a potential, let us study the Lagrangian L = 1 2 m ˙ ~ r 2 + q c ˙ ~ r ~ A ( ~ r ) - ( ~ r ) where ~ r is the position of the particle in cartesian coordinates, ~ A ( ~ r ) is a vector-valued function of the coordinate, φ ( ~ r ) is a scalar function of the coordinate, and q and c are constants. a) Derive the three equations of motion corresponding to this Lagrangian. b) Rewrite the equations of motion as a single vector equation using the curl of ~ A ( ~ r ) and the gradient of φ ( ~ r ). c) Do you recognize these equations of motion?
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set7 - Department of Physics The Ohio State University...

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