Limiting case for an angle in an equation

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In summary, the conversation discusses a problem from Landau course for theoretical physics, volume 2: The Classical Theory of Fields regarding finding the extrema of an expression involving cotΘ. The independent variable for this problem is tetha_0 and setting V and V0 constant is necessary for each case. The conversation also mentions struggling with the problem and requesting advice or a derivation.
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Xsnac
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Homework Statement


7691_F9_E4254_AB9929_EB8_EFE7135_F1_BF765_F8820_D71_ABADB.jpg


Homework Equations


The one in the middle with cot (big tetha)

The Attempt at a Solution


I have no ideea how he finds the limiting cases for V<v0; v0<V and for V> v0/sqrt (1-v0^2) .
The problem is from Landau course for theoretical physics, volume 2: The Classical Theory of Fields. page 35.
I have been struggling with this problem for quite some time but made no real progress. Any bit of advice or even a full derivation step by step would be much appreciated. Is not a homework in the real sense btw. Thank you.
 
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What is the independent variable for finding the extrema of
upload_2016-11-4_14-22-13.png

?
 
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  • #3
TSny said:
What is the independent variable for finding the extrema of
View attachment 108463
?

I would say the independent variable is tetha_0 since for each case we set V and V0 constant.
 
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Xsnac said:
I would say the independent variable is tetha_0 since for each case we set V and V0 constant
Yes. Did you try finding the extrema of the right-hand side of the cotΘ expression?
 

Related to Limiting case for an angle in an equation

1. What is a limiting case for an angle in an equation?

A limiting case for an angle in an equation is a special angle value that causes the equation to behave differently or reach a unique solution. This angle value is often the boundary between two different behaviors or solutions.

2. How do you determine the limiting case for an angle in an equation?

The limiting case for an angle in an equation can be determined by setting the angle value to the boundary value and observing how the equation behaves. The boundary value can be found by analyzing the behavior of the equation as the angle approaches different values.

3. Why is it important to consider the limiting case for an angle in an equation?

Considering the limiting case for an angle in an equation is important because it helps us understand the behavior of the equation and the impact of the angle value on the solution. It also allows us to identify any special solutions or behaviors that may occur at the boundary value.

4. Can there be multiple limiting cases for an angle in an equation?

Yes, there can be multiple limiting cases for an angle in an equation. This can happen when the equation has different behaviors or solutions at different boundary values. In this case, each boundary value would be considered a limiting case for the angle in the equation.

5. How can the limiting case for an angle in an equation be used in real-world applications?

The limiting case for an angle in an equation can be used in real-world applications to identify critical points or values that may have significant impacts on the system being studied. It can also help in making predictions and analyzing the behavior of the system under different conditions.

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