Hamilton’s principle maximises potential energy?

In summary, Hamilton's principle seeks to minimize the difference between kinetic energy and potential energy, with a fixed kinetic energy. This results in the maximization of potential energy. When the limit of kinetic energy approaching zero is considered, the Lagrangian becomes solely the negative of potential energy. This is explained by Feynman in his lectures, particularly in Figure 19-6. However, considering this limit may not be meaningful in understanding the overall concept of maximizing potential energy.
  • #1
3
1
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?
 
  • Like
Likes Delta2
Physics news on Phys.org
  • #3
anuttarasammyak said:
Feynmann does a good explanation around Fig 19.3 in https://www.feynmanlectures.caltech.edu/II_19.html.
Thank you, however, I don't think he said anything about maximization of PE and its meaning?
 
  • #4
Sorry, Fig 19-6 and its around explains it.
 
  • Like
Likes Delta2 and sentai
  • #5
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)?
 
  • #6
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.
 

Suggested for: Hamilton’s principle maximises potential energy?

Back
Top