Papers on Calculus of Variations

In summary, the conversation is about searching for fun and interesting papers related to calculus of variations for a talk. The speaker has been unsuccessful in their search and is asking for suggestions. Another person suggests looking into physics texts, specifically Feynman's Lectures Book 2 and Black Holes, which describe the principle of maximal time. The original speaker clarifies that they are specifically looking for a paper.
  • #1
refind
51
0
I want to give a talk related to calculus of variations. Does anyone know any fun/interesting papers that are somewhat simple to understand?
Could be anything related to calculus of variations, including Lagrangian/Hamiltonian mechanics.
I'm having really bad luck in my search, been trying all afternoon. I find good books, but not good papers. Thanks for the help!
 
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  • #2
refind said:
I want to give a talk related to calculus of variations. Does anyone know any fun/interesting papers that are somewhat simple to understand?
Could be anything related to calculus of variations, including Lagrangian/Hamiltonian mechanics.
I'm having really bad luck in my search, been trying all afternoon. I find good books, but not good papers. Thanks for the help!
Don't know any papers but there are Physics texts that give elementary explanations and examples- non heavy math.
Feyynmann's Lectures Book 2.
Black Holes describes the principle of maximal time.
 
  • #3
I want a paper.
Thanks though
 

What is the Calculus of Variations?

The Calculus of Variations is a branch of mathematics that deals with finding the optimal path or function for a given set of constraints. It involves optimizing a functional, which is a mathematical expression that takes in a function as input and outputs a real number.

What are some real-world applications of the Calculus of Variations?

The Calculus of Variations has a wide range of applications in various fields such as physics, engineering, economics, and biology. Some common examples include finding the shortest distance between two points, determining the optimal shape for a bridge, and minimizing the energy required for a satellite to orbit a planet.

What is the Euler-Lagrange equation and how is it used in the Calculus of Variations?

The Euler-Lagrange equation is a fundamental equation in the Calculus of Variations that helps find the optimal path or function. It is a second-order partial differential equation that is derived from the principle of least action. It is used to determine the necessary condition for a function to be an extremum of a functional.

What are some techniques used in solving problems in the Calculus of Variations?

Some common techniques used in solving problems in the Calculus of Variations include the Euler-Lagrange equation, the method of Lagrange multipliers, and the calculus of variations in several variables. These techniques help to find the optimal solution to a functional by minimizing or maximizing it under given constraints.

What are some challenges faced in solving problems in the Calculus of Variations?

One of the main challenges faced in solving problems in the Calculus of Variations is the non-linearity of the Euler-Lagrange equation, which makes it difficult to find explicit solutions. Additionally, the presence of multiple extrema can make it challenging to determine the optimal solution. Another challenge is the high computational complexity involved in solving problems in higher dimensions.

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