## Including Dissipation in Kinetic Energy of Lagrangian

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, $$B$$.

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

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

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

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.
 PhysOrg.com physics news on PhysOrg.com >> Is there an invisible tug-of-war behind bad hearts and power outages?>> Penetrating the quantum nature of magnetism>> Rethinking the universe: Groundbreaking theory proposed in 1997 suggests a 'multiverse'

 Tags dissipation function, energy, lagrangian

 Similar discussions for: Including Dissipation in Kinetic Energy of Lagrangian Thread Forum Replies Introductory Physics Homework 1 Advanced Physics Homework 3 Introductory Physics Homework 3 Introductory Physics Homework 13 Classical Physics 0