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Retrieved physics discussions and literature describe methods for deriving and justifying Newton's third law of motion from foundational principles such as the homogeneity of space.
Deduction of the Third Law of Motion. The question of the possibility of deducing the third law from the first … conservation of energy (as defined by him) “can be deduced trom Newton’s third law and from the denial of action … and the third law had not been proved, and that the incompatibility with /’s law and the third law was a
# Deriving Newton's Third Law from homogeneity of Space
Tags: newtonian-mechanics, forces, lagrangian-formalism, conservation-laws
- Score: 26
- Views: 10199
- Answers: 3
- Answered: yes
- Asked by: user4235
- Asked: 2011-07-10
- Edited: 2014-05-30
- Site: physics
## Question
I am following the first volume of the course of theoretical physics by Landau. So, whatever I say below mainly talks regarding the first 2 chapters of Landau and the approach of deriving Newton's laws from Lagrangian principle supposing Hamilton's principle of extremum action. Please keep this view in mind while reading and answering my queries and kindly neglect the systems to which Action Principle is not applicable:
If we use homogeneity of space in Euler-Lagrange equations, we obtain a remarkable result i.e. the conservation of momentum for a closed system.
Now, this result, using the form of Lagrange for a closed system of particles, transforms into $ \Sigma F = 0 $ . Now, how from this can we conclude that the internal forces that particles exert come in equal and opposite pairs?
Is it because for 2 particles this comes out as $ F_{1} + F_{2} = 0 $ and we take the forces exerted by particles on o
Everything we examined (2)
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