Limiting case for an angle in an equation

Xsnac · Nov 3, 2016

Homework Statement

Two ellipse diagrams of decay geometry, (a) V < v0 and (b) V > v0, with points A and O, angle theta and max angle labelled; below, printed text giving ranges of the separation angle for each case.

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.

TSny · Nov 4, 2016

What is the independent variable for finding the extrema of

Equation for cot Θ: (V² − V₀² + V² V₀² sin² θ₀) divided by (2V V₀ √(1 − V² sin θ₀)), with the denominator's square root covering 1 − V² and sin θ₀ as printed.

?

Xsnac · Nov 5, 2016

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.

TSny · Nov 5, 2016

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?

Limiting case for an angle in an equation

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

Similar threads