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 vdependent forces can do this – for example, the friction force, μ v , cannot....
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 Fall '11
 Hassam
 mechanics, Force, Mass, Goldstein, Cartesian components, constant vector

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