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Let me begin the question by admitting upfront that my knowledge of physics is limited only to high school and I am extremely rusty with that.

With the above out of the way, I want to understand the following better. So, it seems that the high school description of Newtonian mechanics leaves a lot to be desired (at least the way I understand it). The bigger picture, I am told, is that the dissatisfaction with the high school presentations of the topic can be addressed by using the more rigorous framework of the lease action principle. Anyway, back to my question.

Recently, I realized (after a discussion with a physics student) that I misunderstood something very elementary in my understanding of Newton's formulation of mechanics. My understanding of second law says that the net force on an object equals the mass of the object times the net acceleration the object gets. However, I note that this only defines force and should I take this to be a definition, there really is no "law" here. Could you please demystify this for me? What content should I think second law has when force has not been defined for me?

Again, because I am so inexperienced in physics, do let me know if my question is unclear. Also if this has been answered already, do let me know (and feel free to close the question in that case).

Qmechanic
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Akash Kumar
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    It seems like you are asking two questions here. Are you wanting to know more about N2L, forces, etc., or are you wanting to know more about the least action principle? Either way, both questions don't seem very well-focused. I recommend picking just one question and then making sure that question is clear and objective enough to have a single answer. – BioPhysicist Sep 28 '20 at 20:24
  • I think it is better. I don't think you need to include all of the background about principle of least action. Best to just ask your question. – BioPhysicist Sep 28 '20 at 20:43
  • You have a point. However, I am inclined (perhaps myopically) to leave it this way. This is because, I have been trying to understand the least action principle better (from a mathematical viewpoint). I have been trying to self study the material presented here http://www.math.lsa.umich.edu/~idolga/physicsbook.pdf without much success, I must add. My intention was to also get some motivation for least action this way: perhaps not the sanest thing to do, but I guess maybe worth a try. – Akash Kumar Sep 28 '20 at 21:11
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    Possible duplicates: https://physics.stackexchange.com/q/70186/2451 and links therein. – Qmechanic Sep 28 '20 at 21:27
  • As is well kown, the newtonian formulation and Hamilton's stationary action are mathematically equivalent. In order to compare the two it is necessary to understand how that equivalence comes about. For that see my discussion of Hamilton's stationary action The emphasis is on visualization. – Cleonis Sep 28 '20 at 22:22
  • If all Newton’s Second Law did was define force, it could have no predictive value as an equation of motion. – G. Smith Sep 29 '20 at 00:43
  • @everyone, yes it does answer my question. Thank you for all the help!! – Akash Kumar Sep 29 '20 at 06:31

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