# I Where Does the Term "Kinetic Potential" Come From?

1. Mar 20, 2016

### Niels Bore

I made it to grad school in physics, and then my mind sort of melted and I chose another career. Lately I have been brushing up on math and physics for no clear reason. I decided to join this board so I would have a place to bring my strange questions.

Today I was reading up on Lagrangian mechanics, and I saw the term "kinetic potential" used to describe the difference between the kinetic and potential energies of a system. This is often expressed as L = T - V, where T is kinetic energy and V is potential energy.

Here is what's bugging me: why do they call it "kinetic potential"? Unless I've slipped more than I realize, all the potential for additional kinetic energy is found in the potential energy.

2. Mar 20, 2016

### Vagn

Is it not mean to be Kinetic-Potential energy, where "-" is to be read as minus?

3. Mar 20, 2016

### Niels Bore

That would make more sense.

I found the term "kinetic potential" on p. 229 of Morse and Feshbach, Volume I. Maybe it's a corruption of "kinetic - potential"?

4. Mar 20, 2016

### Staff: Mentor

Many of us don't have that book at hand. Can you quote a sentence or two to give us some context?

5. Mar 21, 2016

### nasu

They use the term "kinetic potential" for what usually is called Lagrangeean or "Lagrange function".
Just a label. An unusual one, maybe.

"We can then express the kinetic potential L = T- V, the difference between
kinetic and potential energies (sometimes called the Lagrange function),
in terms of the q's and their time derivatives..".

6. Mar 21, 2016

### Niels Bore

One of the annoying things about technical education is that we are expected to use terms that haven't been explained. Sometimes the explanations can be very helpful in understanding the thought process behind the material. I thought maybe there was a helpful explanation here.

The passage the previous poster helpfully provided is the one I referred to.

7. Mar 21, 2016

### robphy

One aspect of "potential" is that
its "derivative" gives something that is
(in some sense) "more physical" than the potential itself
because the potential may admit transformations that still lead to the same derivative.
That is to say, the potential is not uniquely determined.

Given the equations of motion, there isn't a unique Lagrangian that leads to those equations

8. Mar 23, 2016

### Niels Bore

I guess if no one here knows the answer, I shouldn't feel too bad.

9. Mar 24, 2016

### vanhees71

Well, I never heard the expression "kinetic potential". Where have you seen it?

10. Mar 24, 2016

### Staff: Mentor

He referred to Morse and Feshbach, "Methods of Mathematical Physics," and nasu gave a quote from it.

I don't remember ever seeing the Lagrangian called "kinetic potential" either, but I've never taught a course in classical mechanics at that level, and it's been a long time since I last studied Lagrangian mechanics, in grad school from Goldstein's book.

That book was published in 1953, so it could simply be old-fashioned terminology that was already falling out of use at the time, but the authors learned it that way and used it out of habit.