Does Lagrangian Mechanics Handle Variable Mass System?

Click For Summary

Discussion Overview

The discussion revolves around the treatment of variable mass systems within the framework of Lagrangian mechanics, contrasting it with Newtonian mechanics. Participants explore the challenges and limitations of applying these mechanics to systems where mass is not constant, questioning the adequacy of existing theories and adaptations.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions how Lagrangian mechanics can effectively handle variable mass systems, suggesting that Newtonian mechanics fails due to the changing nature of the object.
  • Another participant challenges the assertion that Newtonian mechanics cannot address variable mass systems, citing practical examples such as rocketry.
  • A participant expresses skepticism about defining an object with variable mass in the context of Newton's laws, questioning how the second law would apply in such cases.
  • Concerns are raised about the treatment of variable mass systems in various sources, with a specific mention of Wikipedia being deemed incorrect.
  • One participant claims to have seen multiple attempts to adapt Lagrangian formalism for variable mass systems, but believes all have failed, asserting that no satisfactory theory currently exists.

Areas of Agreement / Disagreement

Participants express differing views on the ability of both Newtonian and Lagrangian mechanics to handle variable mass systems, indicating that multiple competing perspectives remain without a consensus.

Contextual Notes

Participants highlight limitations in the existing treatments of variable mass systems, including potential misunderstandings in definitions and the application of fundamental laws of motion.

Pikkugnome
Messages
24
Reaction score
7
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.
 
Physics news on Phys.org
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.
 
Reply
  • Like
Likes   Reactions: Vanadium 50 and vanhees71
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
 
Reply
  • Informative
  • Like
Likes   Reactions: vanhees71 and berkeman
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.
 
Last edited:
Reply
  • Like
Likes   Reactions: weirdoguy

Similar threads

Graduate Flaw in Lagrangian Mechanics for a rotary inverted pendulum system? (Simulation vs. Measured)
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Checking if a stationary point is a minimum using Lagrangian Mechanics
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
Undergrad Can Any Quantifiable Variable Serve as a Coordinate in Euler-Lagrange Equations?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Lagrangian symmetry for the bullet and gun
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How does calculus of variations handle explicit time dependence in Lagrangian?
  • · Replies 7 ·
Replies
7
Views
4K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Lagrangian Mechanics: Variable Mass System?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Effective Potential in Lagrangian & Hamiltonian Mechanics
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad How Does Landau Justify the Additivity of Lagrangians in Isolated Systems?
  • · Replies 9 ·
Replies
9
Views
2K