Applications of Euler-Lagrange Equation

[matpo39]

hey, In my physics class we are now learinging beginging to learn about lagrange ion mechanics and I am a little stuck on the basics of it particularly fermat's principle (dealing with light travel) and applications of the Euler-Lagrange Equation, I can't seem to get many of the problems at the end of the chapter, does anyone know a website or something that has a few worked out examples on how to do these?

thanks

 

[jujio77]

If you are looking for example problems, I would say the best source other than online sources I don't know of would be the Schaums series on Lagrangian Dynamics. They cover many different examples. Of course the best way to learn is to do them yourself!

Good luck.

 

[GSXR750]

for your question! The Euler-Lagrange Equation is a powerful tool in physics and has many applications in various fields. One of the main applications is in classical mechanics, where it is used to derive the equations of motion for a system. This can be applied to various problems, such as finding the path a particle will take in a given potential, or determining the motion of a pendulum.

In addition, the Euler-Lagrange Equation is also used in the field of optics, specifically in the study of geometric optics. This is where Fermat's principle comes in - it states that light will always travel along the path that takes the least amount of time. By applying the Euler-Lagrange Equation to this principle, we can derive the laws of reflection and refraction, as well as understand the behavior of light in different mediums.

There are many resources available online that provide worked out examples of using the Euler-Lagrange Equation. One website that I have found helpful is Khan Academy, which has a series of videos and practice problems on this topic. Additionally, many textbooks on classical mechanics and optics also have examples and practice problems that can help you better understand the applications of this equation.

I would also recommend seeking help from your physics teacher or classmates if you are having trouble with specific problems. Working through problems together and discussing different approaches can often lead to a better understanding of the concept.

Overall, the Euler-Lagrange Equation has numerous applications in physics and with some practice and resources, you will be able to master it. Keep practicing and don't hesitate to reach out for help when needed. Good luck with your studies!