# 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?

Last edited:

Homework Helper
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Since ##f=\frac{\partial D}{\partial \ddot x}##
Do you mean ##f=\frac{\partial D}{\partial \dot x}## ?

• Delta2
mcconnellmelany
Do you mean ##f=\frac{\partial D}{\partial \dot x}## ?
Hmm! It was a typo.

• Delta2