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*From*: curtis osterhoudt <flutzpah@yahoo.com>*Date*: Sat, 23 Jan 2010 07:46:59 -0800 (PST)

""""""""""

P.S.

Does EOM mean "energy of motion"?

Not for me. I

took it to mean *equation(s)* of motion.

"""""""""

Ah, yes. I'm likely the one to have written EOM when he meant Equations of Motion. Sorry about that.

/************************************

Down with categorical imperative!

flutzpah@yahoo.com

************************************/

________________________________

From: David Bowman <David_Bowman@georgetowncollege.edu>

To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>

Sent: Sat, January 23, 2010 8:39:22 AM

Subject: Re: [Phys-l] Landau on Lagrangian

Regarding Bob S's questions:

David wrote:

If we have any other nonlinear function of v^2 (not proportional

to the above linear one or with an affine offset) then

substituting v' + v_0 = v into the nonlinear function of v^2

will not result in the >same function of v'^2 plus a total time

derivative of some function of the dynamical variables, and thus

the resulting EOM will not be frame invariant under GTs.

This does not seem to exclude a linear function of v (ex., L=mv).

Or do I misread your argument?

You are correct that invariance under Galilean boosts *by itself* does not exclude a linear function of v. But that was *already* excluded by the isotropy of space with the argument that L had to be a function of *square speed* v^2. Taking the sqrt of this, namely |v| is *not* a linear function of the velocity vector. It is a nonlinear function of v^2. Such a nonlinear function does not preserve the EOM for Galilean boosts. Note that there is no function f of the dynamical state (r',v',t) such that:

|v| = sqrt(v^2) = sqrt(v'^2) + d/dt(f(r',v',t)) = |v'| + df/dt

when v = v' + v_0 for constant boost velocity v_0.

P.S.

Does EOM mean "energy of motion"?

Not for me. I took it to mean *equation(s)* of motion.

Bob Sciamanda

David Bowman

_______________________________________________

Forum for Physics Educators

Phys-l@carnot.physics.buffalo.edu

https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

**References**:**[Phys-l] Landau on Lagrangian***From:*Stefan Jeglinski <jeglin@4pi.com>

**Re: [Phys-l] Landau on Lagrangian***From:*"Bob Sciamanda" <treborsci@verizon.net>

**Re: [Phys-l] Landau on Lagrangian***From:*Stefan Jeglinski <jeglin@4pi.com>

**Re: [Phys-l] Landau on Lagrangian***From:*David Bowman <David_Bowman@georgetowncollege.edu>

**Re: [Phys-l] Landau on Lagrangian***From:*"Bob Sciamanda" <treborsci@verizon.net>

**Re: [Phys-l] Landau on Lagrangian***From:*David Bowman <David_Bowman@georgetowncollege.edu>

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