Thank you, however, I don't think he said anything about maximization of PE and its meaning?anuttarasammyak said:Feynmann does a good explanation around Fig 19.3 in https://www.feynmanlectures.caltech.edu/II_19.html.
Thanks for pointing it out. Then how should we understand the limit of KE->0, then min(L)=-max(PE)?anuttarasammyak said:Sorry, Fig 19-6 and its around explains it.
Hamilton's principle is a fundamental concept in classical mechanics that states that the motion of a system can be described by minimizing the action, which is the integral of the Lagrangian over time. It is also known as the principle of least action.
Hamilton's principle states that the motion of a system is described by minimizing the action, which is the integral of the Lagrangian over time. The Lagrangian is a function that combines the kinetic and potential energies of a system, and minimizing the action means that the potential energy is maximized.
In Hamilton's principle, the potential energy is maximized because it is combined with the kinetic energy in the Lagrangian. By minimizing the action, the system's motion is described in a way that conserves energy, and maximizing the potential energy is a way to achieve this conservation.
Hamilton's principle is a fundamental concept in classical mechanics that is used to describe the motion of systems. It is a powerful tool for understanding the behavior of physical systems and is used in many areas of physics, including mechanics, electromagnetism, and quantum mechanics.
Yes, there are many real-world applications of Hamilton's principle. It is used in the design of mechanical systems, such as bridges and buildings, to ensure that they are stable and energy-efficient. It is also used in the study of fluid dynamics, where it is used to describe the motion of fluids and optimize their flow. Additionally, Hamilton's principle is applied in the field of optics to design lenses and mirrors for optimal light refraction and reflection.