 12
 3
<Moderator's note: Moved from a technical forum and thus no template.>
Mechanics by Lev D. Landau & E. M. Lifshitz
Chapter 4 Collisions between particles
§16. Disintegration of particles
Problem 3
The angle θ = θ_{1} + θ_{2}
It is simplest to calculate the tangent of θ.
A consideration of the extrema of the resulting expression gives the following ranges of θ, depending on the relative magnitudes of V, v_{10} and v_{20} (for definiteness, we assume v_{20} > v_{10}):
0 < θ < π if v_{10} < V < v_{20},
πθ_{10} < θ < π if V < v_{10},
0 < θ < θ_{10} if V > v_{20}.
So I calculated the tangent of θ and derivative of it
But I can not calculate the extrema, thus I can not solve it...
How to do calculate the extrema?
In addition,
How to do calculate the following?
sinθ_{10} = V(v_{10} + v_{20})/(V^{2} + v_{10}v_{20})
Mechanics by Lev D. Landau & E. M. Lifshitz
Chapter 4 Collisions between particles
§16. Disintegration of particles
Problem 3
The angle θ = θ_{1} + θ_{2}
It is simplest to calculate the tangent of θ.
A consideration of the extrema of the resulting expression gives the following ranges of θ, depending on the relative magnitudes of V, v_{10} and v_{20} (for definiteness, we assume v_{20} > v_{10}):
0 < θ < π if v_{10} < V < v_{20},
πθ_{10} < θ < π if V < v_{10},
0 < θ < θ_{10} if V > v_{20}.
So I calculated the tangent of θ and derivative of it
But I can not calculate the extrema, thus I can not solve it...
How to do calculate the extrema?
In addition,
How to do calculate the following?
sinθ_{10} = V(v_{10} + v_{20})/(V^{2} + v_{10}v_{20})
Attachments

8.5 KB Views: 519

115.3 KB Views: 445
Last edited: