Does Lagrangian Mechanics Handle Variable Mass System?

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SUMMARY

Lagrangian mechanics can address variable mass systems, unlike Newtonian mechanics, which struggles with objects that change mass over time. The discussion highlights that Newton's laws are defined for constant mass objects, making it challenging to apply them to systems like rockets. Various attempts to adapt Lagrangian formalism for variable mass systems have been made, but they have not yielded satisfactory results. The consensus is that a comprehensive theory for variable mass systems remains elusive.

PREREQUISITES
  • Understanding of Lagrangian mechanics principles
  • Familiarity with Newtonian mechanics and its laws
  • Knowledge of variable mass systems in physics
  • Ability to analyze physical systems with changing properties
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  • Research the mathematical formulation of Lagrangian mechanics for variable mass systems
  • Study the limitations of Newtonian mechanics in dynamic systems
  • Explore existing literature on variable mass system theories
  • Investigate applications of Lagrangian mechanics in aerospace engineering
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Physicists, aerospace engineers, and students studying advanced mechanics who are interested in the complexities of variable mass systems and their implications in real-world applications.

Pikkugnome
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How to handle a variable mass system with Lagrangian mechanics? As far as I understand Newtonian mechanics fails, because the object is not constant anymore, it is updated every moment to a new object with different physical properties. I don't immediately see how Lagrangian mechanics can do better.
 
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What makes you think Newtonian mechanics cannot handle variable mass systems? If that were the case it would be difficult to build a rocket to go to the Moon etc.
 
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The first and second law specifically talk about one object. I don't think it is possible to define an object on the fly so to speak as one wishes. What would be the form of the 2nd law, if the object itself was a variable?
 
Pikkugnome said:
The first and second law specifically talk about one object. I don't think it is possible to define an object on the fly so to speak as one wishes. What would be the form of the 2nd law, if the object itself was a variable?
A lot of Internet sources get wrong the treatment of a variable mass system. Not Wikipedia:

https://en.m.wikipedia.org/wiki/Variable-mass_system
 
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I have seen several attempts to adapt Lagrangian formalism for variable mass systems. In my opinion all of them failed. Actually I think that there is no satisfactory theory of variable mass systems at all.
 
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