Why is momentum conserved for non conservative system?

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Momentum is conserved in non-conservative systems, such as inelastic collisions, due to Newton's third law, which states that forces between interacting bodies are equal and opposite. In contrast, energy is not conserved in these systems because it can transform into different types, such as thermal energy due to friction. While total energy remains conserved in an isolated system, specific forms of energy can change, leading to the perception of non-conservation. The principle of least action, as presented by Landau, may struggle to address scenarios involving friction, but it still supports momentum conservation. Ultimately, the distinction between energy types and the uniform nature of momentum arises from their fundamental definitions.
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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?
 
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AlonsoMcLaren said:
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.
 
A.T. said:
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?
 
AlonsoMcLaren said:
So why energy has different types and momentum does not?
Because that's how they were defined.
 

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