# Derivative of Potential with respect to dq/dtWatch

#1
You can derive the Euler Lagrange equation using D’Alembert’s principle. The algebra is annoying but after a lot of messing about you can get to this point fairly intuitively:

-dV/dq - d/dt (dT/d(dq/dt)) + dT/dq = 0

where q is a generalized coordinate with an implied index i (omitted for clarity), and dq/dt is similarly indexed and completely independant from q. T is kinetic energy, and V is potential energy.

Now if you define L = T - V (the Lagrangian formation)

the E-L equation should immediately follow, and it does, except it requires d/dt(dV/(dq/dt))) = 0 and I am not sure why that should necessarily be the case, why can't the potential vary with a particles velocity? (Isn't that what it implies), or is it the case that it indeed it is true but the assumption in the E-L equation is that V is a function of q only.

Note: I know how to prove the EL equation using calculus of variations with hamiltonians principle of least action, and I know its considerably less messy, and more general. However the good thing about this method is it starts from basic newtonian mechanics wheras hamiltonians principle is more of an axiom.
0
5 years ago
#2
Hi there,

While you're waiting for an answer, did you know we have 300,000 study resources that could answer your question in TSR's Learn together section?

We have everything from Teacher Marked Essays to Mindmaps and Quizzes to help you with your work. Take a look around.

If you're stuck on how to get started, try creating some resources. It's free to do and can help breakdown tough topics into manageable chunks. Get creating now.

Thanks!

Not sure what all of this is about? Head here to find out more.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of Stirling
Thu, 26 Sep '19
• Heriot-Watt University
Fri, 27 Sep '19
• Royal Holloway, University of London
Sat, 28 Sep '19

### Poll

Join the discussion

#### Are you attending a Global Climate Strike?

Yes, I'm striking (21)
6.03%
No, but I wanted to/I support the cause (203)
58.33%
No (124)
35.63%