Math Is Fun Forum

Thank you Bob. Do you have any proof or find it by considering vectors movements?

Hi,
Could you please tell me what is operant 60° counterclockwise rotation in this coordination? for example, J is operant of 90° rotation in 90° frame which is exp(jπ/2). I convert 60° rotation in 90° frame to this frame by using the equation we talked about. but I did not get correct answers.

I would be very thankful if you give me hint on this subject.

Dear Grantingriver,
Actually, I have Ph. D in electrical engineer, and like to use this theory in the switching of a converter. I think plain and spherical trigonometry can help me, because in future I may extend this work to 3D switching. I know basics of trigonometry like solving trigonometry equations, some formulas of equivalence, etc all the subject we studied about trigonometry in university. However, generalized trigonometry was totally new to me.  From physical facts, I extracted following equations after posting this thread.
D=√3*v*sin(θ)
H=√3*v*cos(θ+30)
There may be a 3/2 or 2/3 coefficient difference between these and your formulation but it is ok. It depends on voltage vector definition. I really astonished how math matches physical phenomena. thank you again for making me familiar with this subject.
Could you please send me the derivation of these formulas, I also will read the book you refer me to.

thank you again for taking your invaluable time and helping me.

for example suppose my set is 1 1 2 2. if second switch fails the set turn to 1 3 2. there is 1 switch less than or equal to 2^0, two switch LE 2^1 and 3 switches LE 2^2. so first condition is satisfied. Second condition is also satisfied. So, it works.
Now, suppose third switch fails; the set will be 1 1 4. there is 1 switch LE 2^0, two switch LE 2^1 and 3 switches LE 2^2. so first condition is satisfied. But since 4>6/2. this series cannot provide all levels ( numbers between 1 to 6).

Since I have develop this method by thinking and try&error, I am not sure about it. Please inform me if this method has any defect. Thank you

yes. means the system has up to 25 sub-modules.

actually this is a fault tolerant inverter, in which if a sub-module failed. the other modules try to maintain the performance using appropriate control. This is first step to examine that the remained operating circuit can compensate loss of that sub-module or not. Therefore, yes, simple as much as possible.

No, they can be any  positive integer number. But the failed switch is discriminated (provided by fault diagnosis system).

Enjoy your meal

dsPIC30F4011. What I need is that I have to ensure that by existing number, all numbers up to summation of all members can be construct. no need to find specific number. There has to be a simple rule.
like the next number in the series be less than summation of the previous numbers. I thought a lot, but every way has a defect!!

P.S I need the answer (yes or no) in less than 10us.

could you explain more or introduce me a reference.
your help is appreciated.

it steady on 1 after 165, I have examined over 10 points.