Hamilton’s principle maximises potential energy?

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Discussion Overview

The discussion revolves around Hamilton's principle and its implications for potential energy, particularly in the context of minimizing kinetic energy minus potential energy. Participants explore the conditions under which potential energy might be maximized, especially when kinetic energy is negligible.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that Hamilton's principle minimizes kinetic energy minus potential energy and suggests that with fixed kinetic energy, it maximizes potential energy.
  • Another participant references Feynman's explanation in the lectures, noting that while it is informative, it does not explicitly address the maximization of potential energy.
  • There is a correction regarding the specific figure referenced in Feynman's work, with a participant clarifying that Fig 19-6 is more relevant to the discussion.
  • A participant questions the understanding of the limit where kinetic energy approaches zero, proposing that this leads to a minimum of the Lagrangian being equal to the negative of maximum potential energy.
  • Another participant states that Feynman indicates the path of the KE-PE integral should be extreme, but expresses skepticism about the meaningfulness of considering the limit of kinetic energy approaching zero.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of Hamilton's principle and its implications for potential energy maximization, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations in the assumptions made regarding the relationship between kinetic and potential energy, particularly in the context of extreme conditions like kinetic energy approaching zero.

sentai
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Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of potential energy. How to understand the potential energy needs to be maximised?
 
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Sorry, Fig 19-6 and its around explains it.
 
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anuttarasammyak said:
Sorry, Fig 19-6 and its around explains it.
Thanks for pointing it out. Then how should we understand the limit of KE->0, then min(L)=-max(PE)?
 
As Feynman stated we are looking for the path KE-PE integral on which should be extreme.
KE=0 takes place at the top of trajectory in Fig 19-6 but I do not think considering such "limit of KE->0" is meaningful.
 

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