(adsbygoogle = window.adsbygoogle || []).push({}); Can someone please explain this remark in Landau-Lifshitz's *Mechanics* about fields?

On pg. 15, it says that "individual components [of momentum] may be conserved even in the presence ofan external field."

What do they mean, exactly, by "external field?"

I know (or at least IthinkI know) that a given component of linear momentum is conserved if the system is translational invariant in that direction (that is, the Lagrangian does not depend explicitly on that coordinate). But how am I supposed to meld this with the idea of a field?

Landau-Lifgarbagez goes on to say that "...in a uniformfieldin the z-direction, the x and y components of momentum are conserved." I think I'd understand why this is if I had a clearer picture of what's meant by "field."

There is also an exercise at the end of this section that mentions the "fieldof an infinite homogeneous plane." What does that mean? As best I can tell, he is talking about a particle that moves in a plane subject to a potential energy that does not depend on the coordinates parallel to the plane. For example, if the plane in question is the x/y plane, the potential U satisfies

[tex]

\frac{\partial U}{\partial x} = \frac{\partial U}{\partial y} = 0.

[/tex]

Am I right or barking up the wrong tree? Thanks.

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# Can someone please explain this remark in Landau-Lifshitz's *Mechanics*?

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