Why is momentum conserved for non conservative system?

[AlonsoMcLaren]

I am reading Landau's mechanics. He proved that energy and momentum are conserved in an isolated system when we forget about non conservative systems.

But why is energy not conserved in non conservative system, but momentum is? What is the proof?

I know we can show that momentum conservation in non conservative systems, like inelastic collision, by Newton's third law. But if I really want to stick to Landau's formulation, where the principle of least action, not Newton's laws, is the First Principle, how do I explain that momentum is conserved in non conservative systems? Or is the principle of least action simply incapable of handling friction?

 

[A.T.]

But why is energy not conserved in non conservative system, but momentum is?

Energy comes in different types, while momentum doesn't. For an isolated system total energy is conserved just like total momentum is. But the amount of a specific energy type isn't conserved, as energy is converted into other types.

 

[AlonsoMcLaren]

Energy comes in different types, while momentum doesn't. For an isolated system total energy is conserved just like total momentum is. But the amount of a specific energy type isn't conserved, as energy is converted into other types.

So why energy has different types and momentum does not?

 

[A.T.]

So why energy has different types and momentum does not?

Because that's how they were defined.