Hamilton’s principle maximises potential energy?

[sentai]

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?

 

[anuttarasammyak]

Feynmann does a good explanation around Fig 19.3 in https://www.feynmanlectures.caltech.edu/II_19.html.

 

[sentai]

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?

 

[anuttarasammyak]

Sorry, Fig 19-6 and its around explains it.

 

[sentai]

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)?

 

[anuttarasammyak]

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.