How can I be sure that the action has a minimum?

  • Thread starter alialice
  • Start date
  • Tags
    Minimum
In summary, when calculating the minima of an action, it is important to find the extreme or stationary points. The principle of least action is more accurately called the principle of stationary action. In Lagrangian Mechanics, any path that extremizes the action will be a solution to the Euler-Lagrange equation, regardless of whether it is a minimum or maximum. However, if the initial and final points are fixed, the action will have a minimum for the correct classical path, though further confirmation may be necessary from a book.
  • #1
alialice
51
0
When you write an action and then you calculate its minima, how can you be sure that they are minima and not maxima?
Thanks
 
Physics news on Phys.org
  • #2
Usually the phrase, "minimizing the action" is somewhat misused and can make things confusing for this reason. Finding the "extreme points" or "stationary points" of the action is what is important. The "principle of least action" is more accurately termed the "principle of stationary action."

For instance, in Lagrangian Mechanics, any path that extremizes the action, i.e. [itex]\delta S=0[/itex], whether minima or maxima, will be a solution to the Euler-Lagrange equation.
 
  • #3
If the initial and final points are fixed,then action does have a minimum for the correct classical path.But I will have to see a book before conforming it.
 

FAQ: How can I be sure that the action has a minimum?

1. How do you determine if an action has a minimum?

To determine if an action has a minimum, a scientist will typically use mathematical analysis and data to identify the point at which the action reaches its lowest point. This can be done through the use of calculus and optimization techniques.

2. What is the significance of finding the minimum of an action?

Finding the minimum of an action is important because it allows us to understand the optimal conditions for that action. This can help us make predictions and decisions based on the most efficient and effective way to achieve a certain outcome.

3. Can an action have more than one minimum?

Yes, it is possible for an action to have multiple minima. This can happen if there are multiple optimal points or if the action has a complex shape with multiple local minima and a global minimum.

4. How does the presence of noise or variability affect determining the minimum of an action?

Noise or variability can make it more difficult to determine the minimum of an action. It can introduce uncertainty and make it harder to identify the true minimum point. In these cases, scientists may need to use statistical methods to account for the noise and make more accurate predictions.

5. Are there any limitations to finding the minimum of an action?

While mathematical analysis can help determine the minimum of an action, it may not always be possible to find the exact minimum point. This is because some actions may have complex shapes or be affected by external factors that are difficult to account for. In these cases, scientists may need to use approximations or make assumptions to determine the minimum.

Similar threads

B Maximum velocity for projectile motion?
Replies
25
Views
2K
A Stationary Point of Variation of Action
Replies
16
Views
1K
How Does Changing Distance Affect Microwave Path Difference?
Replies
7
Views
536
I Is the Action Always a Minimum in the Principle of Least Action?
Replies
3
Views
1K
How to find the angle where the required pull is minimum?
Replies
25
Views
2K
Finding Absolute Minima & Maxima of a Function
Replies
8
Views
1K
I Understanding Hessian for multidimensional function
Replies
1
Views
2K
I Discussion about least squares method
Replies
2
Views
871
A new take on a relative velocity problem
3
Replies
88
Views
4K
I Which branch of mathematics talks about this?
Replies
13
Views
3K

Hot Threads

Recent Insights

Back
Top