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

  • #1
mcconnellmelany
21
4
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:

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
39,162
8,486
Since ##f=\frac{\partial D}{\partial \ddot x}##
Do you mean ##f=\frac{\partial D}{\partial \dot x}## ?
 
  • #3
mcconnellmelany
21
4
Do you mean ##f=\frac{\partial D}{\partial \dot x}## ?
Hmm! It was a typo.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
39,162
8,486

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

Replies
5
Views
292
  • Last Post
Replies
14
Views
377
Replies
1
Views
250
Replies
6
Views
457
Replies
13
Views
634
  • Last Post
Replies
1
Views
427
Replies
2
Views
318
  • Last Post
Replies
6
Views
694
  • Last Post
Replies
6
Views
578
Top