Finding Minimum Value with Mathematica

[aredy29]

∂ω² = (1-cos²(Δt)e^-2γ(t))/(nTtsin²(Δt)e^-2γ(t))

n,T are assumed as constants. How can I use Mathematica to find the values of Δ and t that will give the minimum values for ∂ω² ?

 

[Bill Simpson]

If I use Expand on your function I get

1/(n T t)((E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2)

Without knowing the signs of n and T we can't know the sign of the result and can't know minimum.

Both Csc^2 and Cot^2 go to infinity at multiples of Pi. Depending on what your gamma function is, either the term with Csc or Cot will win the race to infinity and I believe you can determine the minimum by inspection.

 

[aredy29]

What do you mean with sign of n and T ?

 

[Bill Simpson]

What do you mean with sign of n and T ?

If n*T is negative the whole function will be flipped upside down, what was a minimum would be a maximum, etc.

 

[aredy29]

n and T are integers and always positive.

 

[Bill Simpson]

n and T are integers and always positive.

Then I believe, if you can verify the result from Expand, that n and T can be ignored and you focus on

E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2

If E^(2 gamma[t]) can be < 1 when delta t=Pi then the minimum appears to be -Infinity.