Understanding Lagrangian Action: Tips from a Student

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In summary: Action is defined as the integral of the Lagrangian with respect to time between specified limits. It is a fundamental principle in nature and is essential in all theoretical physics. Feynman's lecture in "The Feynman Lectures on Physics" provides a more thorough explanation.
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rayveldkamp
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Hi, I've just started a course in Classical Mechanics, in 3rd year undergraduate physics, and I'm a bit confused as to what exactly an ACTION is.
All we've been told is that the action, S is defined as the integral from t1 to t2 of the Lagrangian with respect to time.
Thanks in advance

Ray Veldkamp
 
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  • #3
Thanks for the help, I'm sure I'll have plenty more Classical mechanics questions this semester
 
  • #4
It is the essential functional in all theoretical physics...For discrete systems,it is indeed the integral of the function called LAGRANGIAN wrt time between specifed fixed limits.

Daniel.

Adn the extremum principle joining it is the fundamental principle in nature.
 
  • #5
rayveldkamp said:
Hi, I've just started a course in Classical Mechanics, in 3rd year undergraduate physics, and I'm a bit confused as to what exactly an ACTION is.
All we've been told is that the action, S is defined as the integral from t1 to t2 of the Lagrangian with respect to time.
The action is easy enough to define mathematically but its physical meaning is a very difficult thing to understand. I struggle with it. I would highly recommend Feynman's lecture - Chapter 19 in Volume II of The Feynman Lectures on Physics.

AM
 

FAQ: Understanding Lagrangian Action: Tips from a Student

What is Lagrangian Action?

Lagrangian Action is a mathematical concept used in physics to describe the motion of a system. It is based on the principle of least action, which states that the actual path of a system is the one that minimizes the action, a quantity that is defined as the integral of the Lagrangian over time.

How is Lagrangian Action related to Newton's Laws of Motion?

Lagrangian Action provides an alternative way to describe the motion of a system compared to Newton's Laws of Motion. While Newton's Laws focus on forces and accelerations, Lagrangian Action focuses on the energy and motion of a system. However, both approaches lead to the same equations of motion.

What are some common applications of Lagrangian Action?

Lagrangian Action is used in a variety of fields, including classical mechanics, quantum mechanics, and general relativity. It is often used to study the motion of particles, as well as more complex systems such as fluids, electromagnetic fields, and even the entire universe.

How can I use Lagrangian Action to solve problems?

The first step in using Lagrangian Action to solve a problem is to define the Lagrangian for the system. This involves identifying the relevant variables and their associated energies. Then, using the principle of least action, you can derive the equations of motion for the system and solve for the desired quantities.

What are some common challenges when using Lagrangian Action?

One of the main challenges when using Lagrangian Action is identifying the correct Lagrangian for a given system. This often requires a deep understanding of the physics involved and can be difficult for complex systems. Additionally, the calculations involved in solving the equations of motion can be quite complex and time-consuming, especially for systems with many particles or degrees of freedom.

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