Re: Velocity dependent force and Lagrangian
- From: markwh04@xxxxxxxxx
- Date: 5 Jan 2006 13:08:27 -0800
Ass wrote:
> In netwonian mechanics, we can express velocity dependent forces(e.g. air
> resistance, drag) in from of F=kv. It seems that Lagrangian mechanics deals
> with conservative force only. Is it possible to express these forces in form
> of Lagrangian mechanics?
That's the whole point of the Lagrangian formalism!
It generalizes the situation with conservative forces to the more
general situation where the force (F) and momentum (p) may be related
to both the position (r) and velocity (v) in the more general where
F(r,v).dr + p(r,v).dv is a total differential instead of just F(r).dr
(where the ().() denotes scalar product over the N-dimensional
configuration space r = (r1,...,rN)).
The Helmholtz conditions determine what is required for F and p as
functions of r and v for this to occur.
.
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