Find dissipative function for the non-linear force f=-bv^n

[mcconnellmelany]

Homework Statement

For a nonconservative force,
What would be the dissipative function for a force f=-bvⁿ in Lagrangian
(Where v is the velocity)
[#qoute for a nonconservative force f=-bv
The dissipative function is D=-(1/2)bv² ]

Relevant Equations

$\frac{d}{dt}(\frac{\partial L}{\partial \dot x})=\frac{\partial L}{\partial x} - \frac{\partial F}{\partial \dot x}$

For a nonconservative force,
What would be the dissipative function for a force f=-bvⁿ in Lagrangian
(Where v is the velocity)
[#qoute for a nonconservative force f=-bv
The dissipative function is D=-(1/2)bv² ]

Since $f=\frac{\partial D}{\partial \dot x}$ so the dissipative function should be $D=-\frac{1}{n+1}bv^{1+n}$, isn't it?

 

[haruspex]

Since $f=\frac{\partial D}{\partial \ddot x}$

Do you mean $f=\frac{\partial D}{\partial \dot x}$ ?

 

[mcconnellmelany]

Do you mean $f=\frac{\partial D}{\partial \dot x}$ ?

Hmm! It was a typo.

 

[haruspex]

Hmm! It was a typo.

Your answer looks right to me.