Need help with euler langrange equation.

  • Thread starter songhaegyo
  • Start date
  • Tags
    Euler
In summary, the Euler-Lagrange equation is a mathematical formula used to find the function that minimizes or maximizes a certain integral. It is important because it eliminates the need for trial and error and has various applications in fields such as physics, engineering, and economics. The equation can be solved by taking the derivative of the integrand with respect to the function and setting it equal to zero, resulting in a differential equation. Some applications of the equation include finding the path of least action in classical mechanics, optimizing control processes in control theory, and finding the utility-maximizing function in economics. However, it has limitations and assumptions, such as the function being continuous and the boundary conditions being fixed, as well as difficulties with non-different
  • #1
songhaegyo
3
0
Need urgent help with euler langrange equation.

So I've identified the euler langrange equation in my problem as

d/dt (∂L/(∂x: ̇))-∂L/∂x=0

translates to d/dS (∂L/(∂C: ))-∂L/∂C=0

if L is L=43.007 ln(C)-0.0042S^2-3.4339S+1059.37

whereby ∂C:= ∂C/∂S.

How do i solve this?? I am stuck.
 
Physics news on Phys.org
  • #2


You should probably start by calculating some derivatives
 
  • #3


I can't get ∂L/(∂C:)
 
  • #4


Why?
 
  • #5


what do you mean why?

I have no clue how to get ∂L/(∂C:).

I do however get ∂L/∂C as 43.007/C
 

1. What is the Euler-Lagrange equation?

The Euler-Lagrange equation is a mathematical formula that is used to find the function that minimizes or maximizes a certain integral. It is commonly used in the field of calculus of variations and is named after Leonhard Euler and Joseph-Louis Lagrange.

2. Why is the Euler-Lagrange equation important?

The Euler-Lagrange equation is important because it allows us to find the function that minimizes or maximizes a certain integral without having to use trial and error. This makes it a powerful tool in various fields such as physics, engineering, and economics.

3. How do you solve the Euler-Lagrange equation?

The Euler-Lagrange equation can be solved by taking the derivative of the integrand with respect to the function and setting it equal to zero. This will result in a differential equation that can be solved to find the desired function.

4. What are some applications of the Euler-Lagrange equation?

The Euler-Lagrange equation has many applications in various fields. It is commonly used in classical mechanics to find the path of least action, in economics to find the utility-maximizing function, and in control theory to optimize control processes.

5. Are there any limitations or assumptions to the Euler-Lagrange equation?

Yes, the Euler-Lagrange equation has some limitations and assumptions. It assumes that the function being optimized is continuous and that the boundary conditions are fixed. It also has limitations in cases where the integrand is not differentiable or the domain of the function is not compact.

Similar threads

A Hint as to how to solve an integral differential equation
    • Differential Equations
Replies
6
Views
3K
I Understanding Euler Method: Finding Initial Condition of y(0)=1
    • Differential Equations
Replies
7
Views
2K
A Backward Euler technique vs. periodic function: Damping out?
    • Differential Equations
Replies
7
Views
2K
I On the approximate solution obtained through Euler's method
    • Differential Equations
Replies
1
Views
759
I The diffusion equation with time-dependent boundary condition
    • Differential Equations
Replies
8
Views
2K
I Non-Homogeneous Robin Boundary conditions and Interpretations of Signs
    • Differential Equations
Replies
2
Views
1K
Modifying Euler-Lagrange equation to multivariable function
    • Advanced Physics Homework Help
Replies
1
Views
974
Deriving ODEs for straight lines in polar coordinates for a given Lagrangian
    • Introductory Physics Homework Help
Replies
8
Views
221
A Lagrangian form of an equation
    • Differential Equations
Replies
8
Views
2K
A Discretisation of a PDE in Lagrangian coordinates
    • Differential Equations
Replies
4
Views
624

Hot Threads

Recent Insights

Back
Top