Including Dissipation in Kinetic Energy of Lagrangian

Eidos

Hi all

I've found a way to include dissipation in the kinetic energy of the lagrangian for simple systems and I want to know if its ok to do this. My understanding is that dissipation is typically included using the Rayleigh dissipation function which is seperate from the Lagrangian.

The way I've done it is as follows:

Consider a mass-spring-damper with viscous damping co-efficient, [tex]B[/tex].

where [tex][B]=\frac{N.s}{m}[/tex]

The kinetic energy plus dissipated energy is then
[tex]T=1/2M\dot{x}^2 + 1/2 \int B\dot{x}^2 dt[/tex]

The units of the dissipated energy function
[tex][1/2\int B\dot{x}^2dt]=\frac{N.s}{m}\frac{m^2}{s^2}s=Nm[/tex]

which are units of energy.

Is there a problem with doing things this way?

The equations of motion come out exactly the same as when you do things the "normal" way of using a Rayleigh dissipation function.