Recent content by ytht100

It is my own research. I am trying to solve a kind of least-square problem. If you see the link I provided above (http://users.isy.liu.se/rt/andersh/teaching/lmi.pdf) you will understand more what I am talking about. Also you can read the book of Byod...

A=[ 8147 6324 9575 9572 9058 0975 9649 4854 1270 2785 1576 8003 9134 5469 9706 1419]; D=diag([T^(-3)*L^2 T^(-3)*L^2 T^(-1)*L T^0*L^0]); I have matrix A whose first two columns are of the units T^3/L^2, third columns unit is T/L, and the last...

Thank you all for your kind answer. I have figured it out by using the diagram. Kind regards!

Sorry you answer is NOT clear. I have tried everything that I can think of for several days, can you write down specific equations? Thank you very much!

Thank you very much for your kind answer. Yes, I have drawn it. I am NOT seeking a relationship between alpha1 and alpha2. I am seeking relationship between d(alpha1) and d(v1), in which d represents differentiation.

With FIXED SOURCE AND RECEIVER, I have a light incident from fluid 1 with velocity v1 into fluid 2 with velocity v2. Obviously, according to Snell's law, v1/v2=sin(alpha1)/sin(alpha2), where alpha1 and alpha2 are the angles with regard to the vertical line. My question is: how to calculate...

Thanks indeed! You clear up my mind!

I am trying to solve a ray tracing problem. That is all I can say. Other information may not appropriate on this forum. Could you please tell me which part doesn't make sense? Thank you very much!

1, Thank you for reminding me to write {\vec r} as vector, I have made revisions above. However, x, y, and z are NOT independent variables, for example {x^2} + {y^2} + {z^2} = 1. If they are independent, the problem is very easy because \frac{{d{\vec r}}}{{dz}} = \frac{{d(x,y,z)}}{{dz}} =...

I have the following equations: \left\{ \begin{array}{l} x = \sin \theta \cos \varphi \\ y = \sin \theta \cos \varphi \\ z = \cos \theta \end{array} \right. Assume \vec r = (x,y,z), which is a 1*3 vector. Obviously, x, y, and z are related to each other. Now I want to calculate \frac{{\partial...

you should write out the equation in Cartesian coordinate

Please, someone give me a hint.

Thanks a lot! That was clear!

I have a problem of the following picture. x_0, y_0, z_0, V_0, and V_1 are fixed. http://postimg.org/image/6r0ogcx3f/ The travel time is obviously t = \frac{1}{{{V_1}}}{[{({x_1} - {x_c})^2} + D_1^2]^{1/2}} + \frac{1}{{{V_0}}}{[{({x_c} - {x_0})^2} + D_0^2]^{1/2}} According to a high-profile...

I have light incident from plane with velocity v0 into plane with velocity v1. Obviously, according to Snell's law, v0/v1=sin(theta0)/sin(theta1), where theta0 and theta1 are the angles with regard to the vertical line. How to calculate d(theta0)/d(theta1)? There are probably arguments from...