Thank you for the video. Great lesson. Please, how about if one wanted to plot the eigen-*vectors* of a given matrix say, eigenvector, Phi, vs displacement, x, or perhaps Phi vs (x,y) i.e. for a 2D surface plot? For example, in dynamics problem where one is required to plot the normal modes for a 2 degree of freedom mass-spring assembly (3x3 matrix) on a *surface plot*. I have attempted this using the plot function but the results were not as expected compared to calculation I did by hand. Also, I have tried the built-in MATLAB help menu.
Let me make sure we are on the same page here. Let's say you have a single degree of freedom system. xdbldot + 5 xdot + 3 x = f. The characteristic equation would be s^2 + 5s + 3 = 0 The eigen values would then be the solution to the quadratic equation above and the eigenvector would simply be a scalar since the equation is one dimensional. In 2D say you have the equation. zdot = Az where z = [x1 , x2] then your characteristic equation would be solved in a similar fashion to the 1D problem using laplace transforms zdot - Az = 0 Z ( s I - A ) = 0 then det(s I - A ) = 0 would give your characteristic equation and your eigenvalues. Your eigen vectors would then be solved by computing the vectors that solve the equation Z (s I - A) = 0 The eigenvalues themselves are constant and scalar while the eigenvectors as well are also constants but 2D. I'm curious how to generate a plot with constants. Typically a plot is used to generate a figure of some sorts where a parameter varies. For a spring mass damper system, the eigenvalues and eigenvectors are constant and thus do not change with position (x).
Thank you for your prompt response, Doc. And, yes, we are on the same page. And in fact, at first I thought along the same lines as you with respect to the eigen-vectors, that how exactly do you represent them (i.e. constants) on a plot, more so, on a 3D plot especially since they are not related by some function w.r.t displacement, right? Now (and I really wish I could send you some notes and sketches right now instead of just texting which may be quite of a constraint), if we take a mass-spring system, the Amplitude are trivial solutions, hence they are represented as ratios. However, (see W T Thomson (2005), Vibrations, p.129), we can still plot one of the Amplitudes (or eigen-vectors) relative to the other as it were. If you visualise this, it may look like a graph of straight (but inclined) lines ascending or descending from a centre (or reference) horizontal line (kind of similar to the graph of the equation motion in elementary physics). Similarly, this way of representing normal modes of single-degree of freedom in 2D as described above may be extended to represent multi-dof on 3D with phi on, say, z axis while x and y axis remaining orthogonal to z axis. It implies, for example if you had the following as the first eigen-vector (phi): 1 1 1 Then, this first mode will correspond to either a "constant velocity mode" or "constant pressure mode" as the case may be. And a shaded portion representing this eigen-vector on a x-y plane of the 3D surface plot will be raised by equal lengths on the x, y, z axes of a 3D rectangular Cartesian coordinates. I could try to send you a picture of what I mean if you don't mind. Thank you for your time.
I think I get what you're saying and I added a new video. Check it out here. ruclips.net/video/Q64VyOVwcb4/видео.html Comment on that video if I understood what you were saying.
sorry to be so off topic but does anyone know a method to get back into an instagram account..? I was stupid forgot my password. I appreciate any tricks you can give me.
You could technically write your own routine if you like. Finding the eigenvalues involves solving the polynomial equation det(s*I - A) = 0. If you can write a solver that computes s (the eigenvalues) then you could solve the system of linear equations (s*I-A)*v = 0 where v are the eigenvectors. Makes sense?
Dr. Carlos Montalvo I found the characteristics polynomial using charpoly(A) and then used roots(charpoly(A)) in SciLab which further give an equation (A-lamI)X=0 but how to solve this homogeneous system for consistent solutions. Could you please tell me the method? I tried LU decomposition, Gauss's Elimination, Gauss's seidal etc. But all these methods require non zero diagonal elemenys.
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Thank you for sharing this video.
Thank you. It is very useful.
Thank you for the video. Great lesson.
Please, how about if one wanted to plot the eigen-*vectors* of a given matrix say, eigenvector, Phi, vs displacement, x, or perhaps Phi vs (x,y) i.e. for a 2D surface plot?
For example, in dynamics problem where one is required to plot the normal modes for a 2 degree of freedom mass-spring assembly (3x3 matrix) on a *surface plot*.
I have attempted this using the plot function but the results were not as expected compared to calculation I did by hand. Also, I have tried the built-in MATLAB help menu.
Let me make sure we are on the same page here. Let's say you have a single degree of freedom system.
xdbldot + 5 xdot + 3 x = f.
The characteristic equation would be
s^2 + 5s + 3 = 0
The eigen values would then be the solution to the quadratic equation above and the eigenvector would simply be a scalar since the equation is one dimensional.
In 2D say you have the equation.
zdot = Az
where z = [x1 , x2]
then your characteristic equation would be solved in a similar fashion to the 1D problem using laplace transforms
zdot - Az = 0
Z ( s I - A ) = 0
then
det(s I - A ) = 0
would give your characteristic equation and your eigenvalues. Your eigen vectors would then be solved by computing the vectors that solve the equation
Z (s I - A) = 0
The eigenvalues themselves are constant and scalar while the eigenvectors as well are also constants but 2D. I'm curious how to generate a plot with constants. Typically a plot is used to generate a figure of some sorts where a parameter varies. For a spring mass damper system, the eigenvalues and eigenvectors are constant and thus do not change with position (x).
Thank you for your prompt response, Doc.
And, yes, we are on the same page. And in fact, at first I thought along the same lines as you with respect to the eigen-vectors, that how exactly do you represent them (i.e. constants) on a plot, more so, on a 3D plot especially since they are not related by some function w.r.t displacement, right?
Now (and I really wish I could send you some notes and sketches right now instead of just texting which may be quite of a constraint), if we take a mass-spring system, the Amplitude are trivial solutions, hence they are represented as ratios.
However, (see W T Thomson (2005), Vibrations, p.129), we can still plot one of the Amplitudes (or eigen-vectors) relative to the other as it were. If you visualise this, it may look like a graph of straight (but inclined) lines ascending or descending from a centre (or reference) horizontal line (kind of similar to the graph of the equation motion in elementary physics).
Similarly, this way of representing normal modes of single-degree of freedom in 2D as described above may be extended to represent multi-dof on 3D with phi on, say, z axis while x and y axis remaining orthogonal to z axis.
It implies, for example if you had the following as the first eigen-vector (phi):
1
1
1
Then, this first mode will correspond to either a "constant velocity mode" or "constant pressure mode" as the case may be. And a shaded portion representing this eigen-vector on a x-y plane of the 3D surface plot will be raised by equal lengths on the x, y, z axes of a 3D rectangular Cartesian coordinates.
I could try to send you a picture of what I mean if you don't mind.
Thank you for your time.
I think I get what you're saying and I added a new video. Check it out here. ruclips.net/video/Q64VyOVwcb4/видео.html Comment on that video if I understood what you were saying.
Thank you, Doc. I have seen the new video and posted some comments there. Please check it out.
sorry to be so off topic but does anyone know a method to get back into an instagram account..?
I was stupid forgot my password. I appreciate any tricks you can give me.
Thanks..
How can I rotate factors in matlab ( varimax rotation)
I'm not familiar with that property unfortunately.
can you find eigen vectors of a matrix without eig(A) command?
You could technically write your own routine if you like. Finding the eigenvalues involves solving the polynomial equation det(s*I - A) = 0. If you can write a solver that computes s (the eigenvalues) then you could solve the system of linear equations (s*I-A)*v = 0 where v are the eigenvectors. Makes sense?
Dr. Carlos Montalvo I found the characteristics polynomial using charpoly(A) and then used roots(charpoly(A)) in SciLab which further give an equation (A-lamI)X=0 but how to solve this homogeneous system for consistent solutions. Could you please tell me the method?
I tried LU decomposition, Gauss's Elimination, Gauss's seidal etc. But all these methods require non zero diagonal elemenys.
Hey Jasmeet, turns out you can do it with rref. I made a video. This was a really cool idea! Thanks. ruclips.net/video/ssfMqFycXOU/видео.html
Thx a lot
what is your email
i want to contact with you by email
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