Unformatted text preview: = d r /dt is the velocity. We contend that if this is fundamental force of physics, the Newtonian equation of motion must be rewritable as 1 (d/dt)( ∂ L/ ∂ q k . ) = ( ∂ L/ ∂ q k ), where L = T – U, T is the kinetic energy, and U = U(q k . , q k, t). Here q k (t) are generalized coordinates and there are no constraints assumed in the formulation of F . (Since there are no constraints, one may let q k → r .) Show that F can be cast into Lagrangian formulation by finding a U( r , v ). There is a systematic way to do this but it can be done by trial and error. 1 Not all v-dependent forces can do this – for example, the friction force, -μ v , cannot....
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This note was uploaded on 12/29/2011 for the course PHYSICS 601 taught by Professor Hassam during the Fall '11 term at Maryland.
- Fall '11